The Automatic Learning for the Rapid Classification of Events (ALeRCE) Alert Broker

Astronomical alert brokers are a new kind of tool in the interface between astronomy and data science. They face new challenges, including infrastructure, machine-learning (ML), and community integration. This makes them important laboratories for testing new ideas in data science going even beyond astronomy.

In terms of infrastructure, the biggest challenge for astronomical brokers is to ingest, annotate, and classify, in a scalable fashion, the large astronomical alert streams coming from large etendue telescopes such as ZTF or LSST. For example, we have typically received between 10⁵ and 10⁶ alerts night^–1 from the public ZTF stream, associated with 5.1 × 10⁷ objects as of 2021 February. For comparison, LSST is expected to produce about 10⁷ alerts night^–1 and contain more than 10⁹ different objects, which requires a distributed type of database and processing. Additionally, there will be a diversity of survey streaming alerts that must be cross-matched and classified in real time (e.g., ZTF, ATLAS, LSST). Thus, the challenge is to ingest data streams from a diversity of telescopes in a scalable fashion and classify them using their combined information to enable a rapid reaction by follow-up telescopes and a self-consistent analysis.

In terms of ML development, the challenges are diverse. What is an appropriate and relevant taxonomy for the astronomical community? How should we balance classification purity and efficiency? How can we develop ML classifiers and bring them into production in a reasonable timescale? How should we include cross-matched information in these classifiers? How can we train models using data that may be highly unbalanced and not fully representative of the unlabeled data? For example, training a classifier with spectroscopically labeled data will tend to be biased toward the bright end of the magnitude distribution. How can we train in a semisupervised fashion to take advantage of the unlabeled data? How can we train using data from a different telescope with a different set of filters/cadences (i.e., transfer learning and domain adaptation)? How can we train models using synthetic or augmented data? How can we detect outliers in a stream of data? All of these are technically challenging problems that need to be developed, validated with the community, and then brought quickly into production.

Integration with the time-domain ecosystem and its community of users is another important challenge. First, brokers must be connected with other brokers, follow-up infrastructure, and data exploration tools. For this to happen, application programming interfaces (APIs) must be developed, simple interfaces that allow users to interact with different databases using virtual observatory or de facto standards. Second, in order to produce relevant data products and tools, frequent interaction with the community is needed to provide feedback and inject new ideas that can help improve the entire ecosystem. This includes interaction with small to large projects that interoperate with the community of survey telescopes, brokers, TOMs, and follow-up telescopes. A diversity of brokers must be encouraged, avoiding a winner-take-all solution and fostering an environment where new, creative solutions rise faster into production.

The ALeRCE broker is a Chilean-led project that aims to become a community broker for LSST and other large etendue survey telescopes. The project is run by an interdisciplinary team composed of astronomers, computer scientists, and engineers, including faculty, postdoctoral fellows, and students. The broker's concept was first announced in 2017 as the natural continuation of the High cadence Transient Survey (HiTS), in which we used the Dark Energy Camera on the 4 m Blanco telescope to discover supernovae (SNe) in real time by combining tools from high-performance computing and ML (Förster et al. 2016). In 2018, a team of scientists was consolidated, the key requirements were defined, the first version of the front end was developed, a memorandum of understanding was signed with the ZTF project, and the initial funding was secured. In early 2019, a dedicated team of engineers was hired to start building the tools needed to ingest the public ZTF alert stream in preparation for LSST.

ALeRCE started to systematically classify the ZTF stream using ML with astrophysically motivated taxonomies based on their light curves (Sánchez-Sáez et al. 2021) in March 2019 and image stamps (Carrasco-Davis et al. 2020) in July 2019. These classifiers are designed to balance the need for a fast and simple classification with a subsequent but more complex classification. ALeRCE has reported 6162 SN candidates to the Transient Name Server ²³ (TNS), of which 883 have been spectroscopically classified. It has classified 1.1 × 10⁶ objects into a taxonomy that has expanded into 15 classes, including transient, periodic, and stochastic variable sources, and with continuously improving precision and purity. All of ALeRCE's data products can be accessed freely via several dashboards, APIs, or a direct database connection.

ALeRCE has adopted Agile work methodologies, ²⁴ which have been adapted to academic environments by several groups. ²⁵ Adopting this methodology has important implications for the broker, which becomes a continuously evolving product with regular data and code releases. All of the major components become dynamic: the classification taxonomy, as the available data sources grow and the product owners identify new scientific questions; the ML classification models, as new training sets and ideas are brought from development into production; and the tools and products, in order to adapt to the changing requirements of the community of users. This means that special attention needs to be given to version control of the broker pipeline, tools, and data products. This is done via the use of GitHub repositories to track code changes and the Semantic Versioning ²⁶ naming convention for our pipeline and associated data releases.

The outline of this paper is as follows. In Section 2, we introduce the science goals of the ALeRCE broker, including a discussion of the broker taxonomy. In Section 3, we describe the ML classifiers used by our broker. In Section 4, we present the pipeline structure and its associated infrastructure. In Section 5, we discuss our main data products, services, and tools. In Section 6, we present some of the main results. Finally, in Section 7, we draw some conclusions and discuss future directions.

Two important questions that can be answered via the study of transients are: (1) what is the nature of explosive phenomena, and (2) what can they teach us about the dynamics of the universe. Rapid classification is key to answering these questions, since it can facilitate dedicated follow-up observations, either rapid or slow, spectroscopic or photometric. Rapid follow-up is critical to understanding short-lived transients and the progenitors of stellar explosions in general, since it probes the outermost, unprocessed layers of exploding stars and the possible interaction with the circumstellar medium (e.g., Yaron et al. 2017; Förster et al. 2018). Early spectroscopy can be used to measure the composition and velocity structure of their ejecta. Late-time follow-up, either photometric or spectroscopic, probes the nature of the progenitor and explosion mechanism by constraining the composition and velocity structure of the innermost layers of the star (e.g., Fang et al. 2019). Having large samples of classified transient events cross-matched with multiband/messenger or contextual information will help characterize the parameter space and provide clues to new, unrecognized populations of events. Furthermore, the ability to cross-match different streams in real time, e.g., the LIGO and LSST streams, will offer possibilities that can lead to new, unexpected discoveries. These larger and better calibrated samples with well-understood systematics can be used for cosmological distance and/or event rate estimations. Finally, rapid follow-up of gravitational microlensing events can allow the detection of planets with masses and separations resembling those in our solar system (e.g., Bennett & Rhie 1996; Gould et al. 2010), while microlensing events with timescales of the order of years can provide clues about the nature of black holes (BHs) and dark matter (e.g., Green 2016). Moreover, microlensing may allow spectroscopic follow-up of sources that might otherwise have been too faint for spectroscopy (e.g., Bensby et al. 2020).

Some of the important questions that can be answered via the study of variable stars are: (1) what is the nature of these systems and the physical mechanisms of variability, and (2) what can they teach us about the structure and formation of our own galaxy, its satellites, and other galaxies in the Local Group (e.g., Catelan & Smith 2015, and references therein). There are various reasons to obtain a uniform and rapid classification of variable stars. Rapid follow-up of stars entering/leaving the instability strip or changing their pulsation modes could provide new insights into the physics of stellar pulsation (e.g., Clement & Goranskij 1999; Buchler & Kolláth 2002; Soszyński et al. 2014). Detection and follow-up of eclipses in pulsating stars can help provide direct stellar mass measurements (e.g., Pietrzyński et al. 2010, 2012). The detection of eruptive events and the spectroscopic follow-up immediately after the beginning of the eruption can provide new insights into the physics of young stellar objects (Contreras Peña et al. 2017; Connelley & Reipurth 2018). Finally, larger and more distant samples of consistently classified variable stars (e.g., Gaia Collaboration et al. 2019a) will be key to understanding the tridimensional structure and formation history of our galaxy, along with that of its neighbors, ranging from the ultrafaint dwarfs to the Magellanic Clouds (e.g., Dékány et al. 2019; Jacyszyn-Dobrzeniecka et al. 2020a, 2020b; Vivas et al. 2020).

Some of the most exciting questions that can be answered from the study of AGN are: (1) what drives the growth of BHs (Alexander & Hickox 2012), (2) what are the physical mechanisms behind AGN variability (Ross et al. 2018; Sánchez-Sáez et al. 2018), (3) are there intermediate-mass BHs (IMBHs; Mezcua 2017; Greene et al. 2020) with masses between stellar and supermassive BHs (SMBHs), (4) what is the structure and size of AGNs (Lawrence 2016), and (5) what can tidal disruption events (TDEs; Arcavi et al. 2014) teach us about BH properties. Rapid classification could help identify and follow up on optical changing-look AGNs, a population that may unlock numerous clues to BH accretion physics (LaMassa et al. 2015; Graham et al. 2020). Selecting large samples of targets based on their multiband variability for reverberation mapping studies can enable better physical constraints on the BH surrounding medium and distance (Peterson et al. 2004). Fast-cadence data can help assemble large samples of IMBH candidates (Martínez-Palomera et al. 2020), which are known to vary on shorter timescales. The early detection of TDEs can provide independent constraints on the BH properties that drive these phenomena (Komossa 2015). All of the above can be done while simultaneously cross-matching the LSST stream with future surveys that will provide critical additional information, such as eROSITA (Merloni et al. 2012), SKA precursors, IceCube (Abbasi et al. 2009), etc. Finally, exploring larger samples of AGNs that are dimmer and redder can lead to the discovery of new populations of events and a better understanding of the AGN phenomena.

An important component of an automatic classifier is the taxonomy used for classification, which defines the classes into which the alert stream will be classified. Choosing a good taxonomy is about achieving a balance between a reasonably accurate classifier, which depends on finding good training sets and the intrinsic separability of the classes, and meeting the demands of different communities of users. More complex taxonomies can be useful for a larger set of communities, but the addition of subclasses can lead to potentially less accurate classification models. The best compromise between the accuracy of the classifier and the complexity of the taxonomy is difficult to define; therefore, in order to guide our choice of taxonomy, we performed a survey of the taxonomies used in other studies that carried out ML classification of variable astronomical objects.

3.1.1. Light-curve Classifier Taxonomy

First, we consider those works that use only light curves in their analysis. We divide them into those that include both persistent variable and transient sources (Table 1), those that include only persistent variable objects (Tables 5 and 6), and those that include only transient objects (Table 7). We examined four publications that include both transient and persistent variable objects in their taxonomy, 22 publications that include only persistent variable objects, and eight publications that include only transient objects. There were 19 different sources of observational data, mostly for persistent variable sources (Table 8), and five sources of synthetic data (Table 9).

Table 1. Light Curve–based ML Classifiers that Include Both Transient and Persistent Variable Objects

Reference	Data Source	Data Type	No. of Classes	Classes
Sánchez-Sáez et al. (2021)	ZTF	Observed	15	SN Ia, SN Ibc, SN II, SLSN,
(See Section 3.3)				AGN, QSO, blazar, CV/nova, YSO,
				DSCT, RRL, Ceph, LPV, E,
				periodic–other
Boone (2019)	PLAsTiCC	Simulated	14	AGN, RRL, E, Mira, M dwarf, ML,
				TDE, kN, SN Ia, SN Ia-91bg,
				SN Iax, SN Ibc, SN II, SLSN-I
Martínez-Palomera et al. (2018)	HiTS	Observed	8	NV, QSO, CV, SN, DSCT, E, ROT, RRL
Narayan et al. (2018)	OGLE, OSC	Observed	7	SN, BPer, RRL, LPV, Ceph, DSCT, DPV
D'Isanto et al. (2016)	CRTS	Observed	6	CV, SN, blazar, AGN, M dwarf, RRL

Note. Note that Sánchez-Sáez et al. (2021) is an accompanying publication where we describe the ALeRCE light-curve classifier in more detail.

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A large diversity of taxonomies was found, with fewer classes in general being used in the last 5 yr with respect to older works. This may be due to the appearance of more exploratory efforts in recent years, which look for variations from more traditional classification methods while using fewer classes for simplicity. We found more classes of persistent variable objects of stellar origin, probably because of the relative abundance of curated light-curve training sets for these classes. The synthetic data sources were applied mostly for transient data, probably because of the relative difficulty in finding large numbers of observed transients. A brief description of the classes is included in the Appendix. The pulsating star variable classes included in the previous publications are shown in Tables 10 and 11, other stellar variable sources in Table 12, SMBH-related sources in Table 13, and transients in Table 14.

In general, there are certain families of objects that seem to be included consistently among most classifiers but whose decomposition into subclasses varies greatly. Taking this into account, we have decided to develop a hierarchical classifier that groups families of classes and will gradually be refined as the amount and quality of the data grow (Sánchez-Sáez et al. 2021). The first level of the classifier considers transient, periodic, and stochastic variable phenomena. In the second level, the transient branch divides into (class name abbreviations in parentheses) the Type Ia SN (SN Ia), Type Ib and Ic SN (SN Ibc), Type II and IIn SN (SN II), and superluminous SN (SLSN) classes. The periodic branch divides into the eclipsing binary (E), δ Scuti (DSCT), RR Lyrae (RRL), Cepheid (Ceph), long-period variables (LPVs, including Miras and semiregular and irregular variables), and other (periodic–other) classes. The periodic–other class corresponds to periodic objects that are not members of the E, DSCT, RRL, Ceph, or LPV classes. The stochastic branch divides into host-dominated AGNs, core-dominated AGNs, quasi-stellar objects (QSOs), blazars, cataclysmic variables and novae (CV/nova), and young stellar objects (YSOs).

ALeRCE's current classification taxonomy is shown in Figure 2. This figure draws inspiration from the variability diagram of Eyer & Mowlavi (2008), most recently updated in Gaia Collaboration et al. (2019b) but significantly simplified and with a more observationally based hierarchy, more resolution in the transient classes, and less resolution in the stellar variability classes. The reason for having more resolution in the transient classes is that in many cases, the reaction time for the photometric or spectroscopic follow-up of these classes needs to be fast, e.g., to get spectroscopic confirmation or characterize a short-lived phase of evolution, while for the persistent variability classes, it is not as common to require fast follow-up. Thus, our main goal is to provide a first filter for the expert communities to explore further and classify into more complex taxonomies in more branches of the classification tree.

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3.1.2. Stamp Classifier Taxonomy

In order to compile training sets, we use only sources observed by ZTF whose labels have been cross-matched from different catalogs available in the literature or compiled by our collaboration. For each catalog, we define a function that maps the catalog's taxonomy into our own taxonomy, allowing us to aggregate labels from different catalogs into a unified taxonomy. Then, we assign a priority order that defines which labels to use in case of disagreement between catalogs. These priorities are based on discussions with community experts, a critical analysis of the methods that were used to classify objects (e.g., manual versus automatic), and an analysis of which catalogs tend to disagree more with other catalogs from a visual exploration of catalog label matrices (similar to confusion matrices but with rows and columns as the classes in each catalog, potentially with different taxonomies).

The catalogs we use to extract labels are, in order of priority,

• 1.  
  the cataclysmic variables catalog, compiled by Abril et al. (2020), including Ritter & Kolb (2003);
• 2.  
  ROMABZCAT, the multifrequency catalog of blazars from Massaro et al. (2015);
• 3.  
  the catalog of type I AGNs from Oh et al. (2015);
• 4.  
  the Million Quasars Catalogue from Flesch (2019);
• 5.  
  the spectroscopically classified SNe in the TNS; ²⁸
• 6.  
  the objects classified as YSOs in Simbad (Wenger et al. 2000);
• 7.  
  the CRTS catalog of northern periodic sources (Drake et al. 2014);
• 8.  
  the CRTS catalog of southern periodic sources (Drake et al. 2017);
• 9.  
  the LINEAR catalog of periodic variables (Palaversa et al. 2013);
• 10.  
  the Gaia Data Release 2 (DR2) catalog of variable stars (Mowlavi et al. 2018); and
• 11.  
  the All-Sky Automated Survey for Supernova (ASAS-SN) catalog of variable stars (Jayasinghe et al. 2019).

This classifier computes classification probabilities for objects with ≥6 detections in g or r. We represent individual light curves as a vector of features compiled from the literature and new features developed by the ALeRCE collaboration as described in Sánchez-Sáez et al. (2021). One of the most relevant new features comes from an irregularly sampled autoregressive model (IAR) introduced in Eyheramendy et al. (2018), which is able to estimate autocorrelation in irregularly sampled time series in a statistically robust way. The classification is done in a hierarchical fashion using a balanced random forest classifier, ²⁹ which, in our tests, achieved better accuracies than recurrent neural networks. As described before, a given object will be first classified as either periodic, stochastic, or transient and subsequently refined into 15 different classes as described in Section 3.1. The confusion matrix associated with this classifier can be seen in Figure 3, described in Sánchez-Sáez et al. (2021).

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Inspection of ZTF image stamps suggests that it should be possible to classify alerts based on the first detection set of stamps (see Section 3.1.2). Therefore, we designed and trained a stamp classifier based on a convolutional neural network with the main motivation of finding SN candidates, using as input the information contained in the first alert, including the science, reference, and difference stamp set, as well as other metadata, such as spatial location and data quality metrics.

The stamp classifier (Carrasco-Davis et al. 2020) is able to discriminate among five classes, SNe, AGNs, variable stars, asteroids, and bogus alerts, achieving 90% accuracy on a balanced test set and a recall of 81% among spectroscopically confirmed SNe from TNS. To improve the model interpretability, we added a regularization term that maximizes the entropy of the predicted probability for each class, enhancing the different certainties for each prediction. This model is currently running on ZTF alerts, and its results are publicly available in the ALeRCE SN Hunter at https://snhunter.alerce.online (see Section 5.2.1). The confusion matrix associated with this classifier can be seen in Figure 4, reproduced from Carrasco-Davis et al. (2020).

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In order to evaluate the classifiers that will go from initial model training into production, we use a combination of metrics and tests that take into account the labeled and unlabeled data. We have found this to be relevant when using a labeled training set known to be nonrepresentative of the unlabeled data. First, we compute the test set classification balanced (averaged per class) accuracy (ratio between correct and total labels) and F1 score (the harmonic mean between precision and recall) to take into account the accuracy, precision, and recall of the classifier while considering the class imbalance, which is very important when using observational data as training sets. Second, we look at the confusion matrix to search for signs of overrepresentation of certain classes that may not be evident in the balanced accuracy. Third, for the light-curve classifier, we look for classification biases with certain relevant variables, e.g., looking for a relatively constant recall versus apparent magnitude relation for individual classes when no significant bias exists. Fourth, we compare the expected and inferred spatial and class distributions of the unlabeled data to discard models using astrophysical knowledge. For example, if the classification model were correct, one would expect the spatial distribution of the different classes to follow known patterns, such as that most Galactic classes should be concentrated around the Galactic plane, extragalactic classes should be homogeneously distributed outside the Galactic plane due to extinction and source confusion, and asteroids should be distributed around the ecliptic. Additionally, we would expect the distribution of class labels in the unlabeled set to follow known population ratios; for example, we expect SNe Ia to be more abundant than SNe Ibc. Therefore, the final choice of a classification model is made considering all of these metrics and tests before the model is brought into production, i.e., applying the model using the available infrastructure with our latest pipeline for nightly operations.

As a consistency check between the two aforementioned classifiers, we compare the distribution of classes of the stamp classifier among those objects classified by the light-curve classifier. In Figure 5, we show a matrix of stamp and light-curve classifier classes, normalized along the light-curve classifier classes. We can see that there is overall agreement between the two classifiers, which highlights the complementarity between our two classifiers and emphasizes the value of using the image stamps for early classifications, as shown in Carrasco-Davis et al. (2019).

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Outlier/novelty detection refers to the automatic identification of abnormal or unexpected phenomena embedded in data (Faria et al. 2016). We are developing outlier detection methods experimentally to focus on two problems: the discrimination of outlier clusters of time series or image stamps, i.e., cohesive and representative sets of examples associated with interesting phenomena that are not characterized in the current training database, and the detection of unexpected events occurring within a particular time series. To solve the first problem, we are developing online one-class/semisupervised outlier detection methods (Schölkopf et al. 2001; Chapelle et al. 2009; Reyes & Estévez 2020) to find similarities between objects and automatically detect outlier phenomena. We are addressing this problem from three different perspectives: using autoencoders, generative adversarial networks, and one-class neural networks. To find unexpected events within time series, we are using robust online nonlinear filters (Liu et al. 2011; Huentelemu et al. 2016). Traditional methods, such as Kalman and kernel filters, are being extended to incorporate measurement uncertainties, the heteroscedasticity of the noise, and the use of state space formulations where states are unevenly separated in time.

For both problems, active-learning techniques (Zhu et al. 2003) are being explored to select sets of the most uncertain objects and/or events to be shown to human experts. We are aiming to use information theoretical feature selection (Estévez et al. 2009) and feature extraction methods to reduce dimensionality and generate visualizations that can be presented to the experts.

The ZTF alerts are sent as Avro packets, ³¹ a data serialization format that contains associated image stamps, metadata, and information related to previous detections as described in https://zwickytransientfacility.github.io/ztf-avro-alert/schema.html. We use Apache Kafka, ³² a framework for working with streaming data, to receive the ZTF alert stream and communicate information between the different steps of our pipeline as independent Kafka topics. We use an Apache Zookeeper cluster with a replication factor of 3, following recommended practices, and three independent machines of Kafka consumers that are responsible for reading data from the alert queue. We have set up a Kafka cluster in Amazon Web Services (AWS) to manage different topics associated with different steps in the pipeline. Assigning different topics for each step in the pipeline has the advantage of allowing for alerts to be grouped in different batch sizes optimized for performance. For example, querying the database for several objects simultaneously can be faster than doing it sequentially for a list of objects depending on the type of query, or, in the case of cross-matching, it may be more efficient to group alerts by their spatial location if the external catalog is stored hierarchically, e.g., a tessellation of the sky. Another advantage is that we can configure each topic independently for performance, e.g., using different numbers of Kafka partitions per topic.

We have tested different configurations of Kafka producers to mimic an LSST-like stream of data, and we have found that a cluster of three Kafka consumers with 12 partitions each is capable of ingesting all of the different topics at a rate of 119.7 MB s^–1, that is, about three times faster than the average alert production rate expected for LSST.

As alerts arrive, we store the original Avro files in AWS Simple Storage Service (S3) buckets for future analysis and extract a selection (in order to limit the size of the database) of the fields contained in these packets to be added directly to a database using a PostgreSQL database engine. As the data are processed and object alerts aggregated, we add different statistics to different tables. The main tables in our database are as follows.

• 1.  
  The object table, which contains basic filter and time-aggregated statistics, such as location, number of observations, and times of first and last detection.
• 2.  
  The magstats table, which contains time-aggregated statistics separated by filter, such as the average magnitude or initial magnitude change rate.
• 3.  
  The detection table, which contains the object light curves, including their difference and corrected magnitudes and associated errors separated by filter (see Section 4.4).
• 4.  
  The non_detection table, which contains the limiting magnitudes of previous nondetections separated by filter.
• 5.  
  The feature table, which contains the object light-curve statistics and other features used for ML classification that are stored as json files in our database.
• 6.  
  The xmatch table, which contains the object cross-matches and associated cross-match catalogs.
• 7.  
  The probability table, which contains the object classification probabilities, including those from the stamp and light-curve classifiers and different versions of these classifiers.
• 8.  
  The taxonomy table, which contains details about the different taxonomies used in our stamp and light-curve classifiers, which can evolve with time.

A webpage containing an updated description of the different tables can be found at https://alerce.science. As the volume of alerts grows for different projects, we expect to migrate some of the previous tables to NoSQL database engines such as Cassandra or MongoDB. After ingestion, the alerts undergo the processing steps described next.

When an alert from a previously unreported object arrives, its first available image stamps are used to classify it as either SN, AGN, variable star, asteroid, or bogus, as explained in Section 3.4. Note that if the first detection from an object did not pass the ZTF real/bogus test but a subsequent detection did, the first available image stamp will not be from the former. This stamp classification is done within 1 s of the alert being received and is automatically available in our database and the SN Hunter tool (see Section 5.2.1), if the candidate is consistent with being an SN. The details of the stamp classifier are described in a parallel publication (Carrasco-Davis et al. 2020).

As explained before, ZTF alerts are produced when a science image contains a significant change with respect to a reference image after aligning, scaling, convolving, and subtracting the reference image from the science image. Flux differences with respect to the reference image are reported as difference magnitudes, and an associated flag (isdiffpos) is included to indicate whether the difference is positive or negative. In the case of ZTF, a reference image is defined by a unique reference field identifier (rfid). If the source was present in the reference image, it is possible to recover its actual apparent magnitude from the difference and reference magnitudes. We do this correction when the nearest cataloged object is closer than 14 (distnr < 1.4), providing a flag to indicate whether we think the object is extended based on PanSTARRS and ZTF shape parameters. The actual apparent magnitude, m_corr, and associated errors, δ m_corr, in the case of a pointlike source that was present in the reference are the following:

$$\begin{eqnarray}\begin{array}{rcl}{m}_{\mathrm{corr}} & = & -2.5{\mathrm{log}}_{10}\left({10}^{-0.4{m}_{\mathrm{ref}}}\right.\\ & & +\left.\mathrm{sgn}\,{10}^{-0.4{m}_{\mathrm{diff}}}\right),\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\delta {m}_{\mathrm{corr}}=\displaystyle \frac{{\left({10}^{-0.8{m}_{\mathrm{diff}}}\delta {m}_{\mathrm{diff}}^{2}\left[-{10}^{-0.8{m}_{\mathrm{ref}}}\delta {m}_{\mathrm{ref}}^{2}\right]\right)}^{0.5}}{{10}^{-0.4{m}_{\mathrm{ref}}}+\mathrm{sgn}\,{10}^{-0.4{m}_{\mathrm{diff}}}},\end{eqnarray} \tag{ 2 }$$

where m_ref is the magnitude of the object in the reference image, m_diff is the magnitude associated with the absolute flux difference between the science and reference images, $\mathrm{sgn}$ is the sign of the difference (isdiffpos), δ m_ref is the error associated with the reference magnitude, and δ m_diff is the error associated with the difference magnitude. Note that we provide both the original and corrected photometry. For the corrected photometry, we include errors values with and without the term inside square brackets in Equation (2) that originates from the correlation between the reference and difference fluxes (see derivation in Appendix).

It is important to note that if the difference flux is equal to the reference flux and the sign of the difference is negative, both the corrected magnitude and associated errors will diverge, which is a limitation of using a logarithmic scale for difference fluxes. This should normally not occur, since an alert is triggered only when there is a significant difference with respect to the reference. However, if the reference image contains a transient source, the difference flux can eventually become exactly minus the reference flux, and the corrected flux is zero, which will lead to divergences depending on the noise. We treat these cases by assigning values of 100 to the corrected magnitudes and their associated errors.

We discuss in detail the derivation of these formulae, how to include the effect of a change in the reference image, and how we treat extended sources in the reference image in Appendix.

A cross-match step runs with the stamp classifier and light-curve correction, querying external catalogs in order to extract additional information about the objects of interest. The ZTF alert packets already contain the nearest solar system, PanSTARRS, and Gaia cataloged sources. In addition to this information, we query WISE and SDSS in order to obtain infrared and spectroscopic information, if available, which can be critical to better constraining some of the classes included in our taxonomy. Additional catalogs will be included as they prove relevant. These queries are done using the CDS cross-match API, ³³ which can handle sufficiently large streams if alerts are grouped in batches around the same region of the sky before querying.

With the corrected light curves, we can compute light-curve characteristics or features based on both the detections and nondetections of a given object, as well as available cross-matches. Advanced light-curve features are only triggered for objects with ≥6 detections in g or r. The features computed are a significantly extended version of the FATS library (Nun et al. 2017), called Turbo FATS, that is optimized for computation speed and adds several new features. A description of these features, which are contained in the feature table of our database, can be found in Sánchez-Sáez et al. (2021).

Objects having computed features are then processed by the light-curve classifier described in Section 3.3. The results of this classifier are obtained within a few tens of seconds from ingestion for 95% of the objects. For a larger stream, this could be maintained by scaling the infrastructure given the embarrassingly parallel nature (i.e., no need of communication between parallel tasks) of the light-curve correction, feature computation, and light-curve classification tasks between different alerts. The current model used for the light-curve classifier is a hierarchical balanced random forest, as described in Sánchez-Sáez et al. (2021).

After the light-curve classification step, we perform an outlier detection step, which, as of 2021 February, is being actively developed experimentally (see Section 3.7).

After the nightly ingestion and processing of the alerts, we perform a series of database integrity tests during the day. This consists of reanalyzing the Kafka topic associated with the last night of observations to check that no alerts were lost during the processing due to unexpected errors. If any alerts were missed during the night, we add them to a specially created Kafka topic that is then processed by our pipeline until no missing alerts exist.

The ALeRCE data products can be divided into several categories: the tables of a database, a repository of Avro files, a repository of Jupyter notebooks, an output stream of annotated and classified alerts, a GitHub repository with our open-source code, a Grafana dashboard to monitor the status of the pipeline, our main website, documentation websites, and tutorial videos for new users. We provide a brief description of each of them in what follows.

5.1.1. Database

5.1.2. Avro Repository

5.1.3. GitHub Repositories

5.1.4. Use-case Jupyter Notebooks

5.1.5. Output Stream

5.1.6. Grafana Dashboard

5.1.7. Main Website, Documentation, and Tutorial Videos

Apart from the previous data products, several services are provided to facilitate the exploration of the ZTF stream and associated objects. They are divided into web interfaces, which are websites that allow the simple exploration of the alert stream, and APIs, which power the previous web interfaces and allow for the flexible integration of ALeRCE into the time-domain ecosystem.

5.2.1. Web Interfaces

ALeRCE Explorer ( http://alerce.online ). The ALeRCE explorer is the main tool to explore the astronomical objects recovered from the ZTF alert stream. Its landing page consists of two main sections: the Search and Results sections (see Figure 7). The Search section is where users can filter objects by selecting their unique identifier or different combinations of classifier, class, class probability, number of detections, and sky coordinates. The Results section is where the results of the filtered objects are shown, sorted by classification probability or other variables. Clicking on an individual object will take the user to the object view page (see Figure 8).

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The object view page is divided into two tabs, the General Information and Cross Matches tabs, with different panels each (see Figure 8). In the General Information tab, users can see some basic statistics about the object, generate a finding chart, query different catalogs at the position of the object (the NASA Extragalactic Database (NED), Simbad, TNS, PanSTARRS, or SDSS), or quickly see basic TNS information about the object. The user can see the object's light curve, including detections and nondetections, with the capability of plotting the raw difference light curve, a corrected apparent magnitude (which includes the contribution of the reference image), or a folded version of the corrected apparent magnitude using the best-fitting period. The light-curve information can be downloaded as comma-separated values (CSVs), and every point in the light curve can be hovered over to see more information or clicked on to show its associated image stamp. HiPS images and catalogs around the position of the object are shown using Aladin (Bonnarel et al. 2000), with superimposed NED and Simbad clickable objects. The science, reference, and difference image stamps associated with any point in the light curve can be shown in the stamps section, where the stamps can be explored by selecting different dates or hovering over them, seen in full screen, or downloaded as fits files. The full Avro packet information can also be explored. The classification probabilities are shown in the stamp and light-curve classifier tabs, where a radar plot is used to show the class probabilities assigned by the light curve– or stamp-based classifiers, if available. Finally, in the Cross Matches tab, users can see all of the cross-matches contained in the catsHTM set of catalogs for a given separation, which can be selected manually with a sliding bar (see Figure 9).

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The ALeRCE explorer is where most of our web development has been focused, including new tools, as requested by our community of users, but also new sources of data that in the future will allow for the multistream exploration of astrophysical objects. We are developing a modular data exploration library that will be gradually expanded to include new sources of streaming data. ³⁴ This library is used for a new version of the ALeRCE explorer that was being tested as of 2021 February, which is connected to a new database and can be previewed in http://stage.alerce.online.

SN Hunter ( https://snhunter.alerce.online ). The SN Hunter platform allows users to visualize and explore the best and most recent SN candidates (see Figure 10). These candidates are obtained using the convolutional neural network that powers the ALeRCE stamp classifier and can be seen in the SN Hunter just seconds after being received from ZTF. Users can see the spatial distribution of the candidates in celestial coordinates and in comparison to the Milky Way plane or the ecliptic, as well as a table that shows them sorted by classification probability, discovery date, or number of observations. Selecting a candidate displays an Aladin HiPS image at the location of the object, as well as the science, reference, and difference images contained in the Avro file. The candidates's unique identifier, coordinates, and first observation properties and the properties of the closest PanSTARRS object are also shown, as well as links to the ALeRCE explorer for the same object or for NED, TNS, and Simbad sources around the position of the object. Users can also see the full alert information contained in the original Avro file of the alert by clicking the Full Alert Information button.

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A key feature of the SN Hunter is the ability to receive feedback from users who have logged in. If a candidate appears to be bogus, users can label the candidate as such to further enhance the training set. Moreover, if the candidate appears to be an SN or extragalactic transient, the user can label it as a possible SN to be sent to the ALeRCE reporter tool (see below). The list of possible SNe can then be explored by the team with our reporter tool, which can then be used to submit targets to the TOMs for follow-up. We regularly compute user labeling metrics in order to provide feedback or identify potentially malicious labeling, and we can use more than one label per object in order to prevent accidental labeling.

Reporter ( https://reporter.alerce.online ). The ALeRCE reporter tool is a platform that serves to manage user feedback in general (see Figure 11). As of 2021 February, it served three purposes: to manage the feedback provided by the SN Hunter interface, to connect with the TOM Toolkit interface, and to manage internal data classification challenges. The user feedback provided via the SN Hunter consists of bogus alert labels for alerts that appear to be bogus and possible SN alert labels for alerts or groups of alerts that appear to be originated by extragalactic transients. The connection of SN candidates with the TOM Toolkit interface is also done from the reporter tool, sending users to the TOM Toolkit interface after clicking on a reported candidate. Finally, the reporter tool can be used to create data challenges, manage associated user entries, produce metrics and confusion matrices, and show leader boards as in Kaggle. The data challenges are key for the collaboration's periodic hackathons, where we set different classification challenges that motivate the ML team to develop new ideas and tools.

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TOM Toolkit Plug-in ( https://tom.alerce.online ). This platform is used to manage and submit candidates to the TOM Toolkit (https://lco.global/tomtoolkit/). Users that have access rights to the ALeRCE reporter can connect with the TOM Toolkit via this interface, allowing them to submit observational requests with detailed instrumental specifications to the queue of different observatories.

Cross-match Service ( http://xmatch.alerce.online ). ALeRCE provides a cross-match service that allows users to submit an arbitrary CSV file with objects and coordinates of their favorite targets (see Figure 12). After a file is uploaded, the user is asked to select the names of the identifier, R.A., and decl. columns. After this is done, the closest objects in ZTF are returned, adding several columns from the ALeRCE object table to the submitted objects. A paginated table is shown for exploration, and the output can be downloaded as a CSV file.

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5.2.2. APIs

All of the interactions between the web interfaces and the database or the Avro/stamp repository are done via APIs. These APIs serve most of ALeRCE's data exploration tools following the principle of maximizing the modularization of our different services. They are also the key elements that will allow ALeRCE to integrate seamlessly with the astronomical time-domain ecosystem. These APIs are documented on the ALeRCE API Documentation website: https://alerceapi.readthedocs.io/en/latest/. Note that as of 2021 February, a new API was being tested that is better documented, easier to use, and connected to an entirely redesigned database (preview at http://dev.api.alerce.online/). Here we describe the services available as of 2021 February.

ZTF Database Access Service ( http://ztf.alerce.online ). This service allows users to query the ALeRCE database tables without needing any authentication. This API includes services to query objects filtered by unique object identifier, number of detections, class, class probabilities, coordinates, or detection times. Users can also get the associated SQL command for a given query, all detections for a given object, all nondetections for a given object, the classification probabilities for a given object, or the features used as input for the ML classifiers for a given object. The documentation can be found at https://alerceapi.readthedocs.io/en/latest/ztf_db.html. This service is used in the ALeRCE explorer and the SN Hunter (see Section 5.2.1).

Avro/Stamps Service ( http://avro.alerce.online ). This service allows users to access the alert Avro files and their associated stamps. The input is the unique object identifier and the unique stamp identifier. Users can get the Avro file, a specific field from an Avro file, or the science, reference, and difference image stamps contained in an Avro file. The documentation can be found at https://alerceapi.readthedocs.io/en/latest/avro.html. This service is used in the ALeRCE explorer and the SN Hunter (see Section 5.2.1).

ZTF Cross-match Service ( http://xmatch-api.alerce.online ). This service allows users to submit an arbitrary catalog and get the nearest ZTF sources and their separation and properties. It is used in the cross-match interface (see Section 5.2.1).

catsHTM Cross-match Service ( http://catshtm.alerce.online ). This service allows users to do cone searches to a given location using the catsHTM catalogs (Soumagnac & Ofek 2018). This includes cone searches returning all objects closer than a given distance from all or a specific catalog or only the closest object from all or a given catalog. This service is used in the ALeRCE explorer Cross Matches view (see Section 5.2.1). The documentation, also indicating a list of all available catalogs, can be found at https://alerceapi.readthedocs.io/en/latest/catshtm.html.

TNS Cross-match Service ( http://tns.alerce.online ). This service allows users to query TNS information about an object centered around a given position in the sky. It queries the TNS API and returns the TNS name, type, and redshift, and it is used by the ALeRCE explorer General Information tab (see Section 5.2.1).

Finding Chart Service ( http://findingchart.alerce.online ). This service provides a finding chart associated with a given object's unique identifier. It returns a PDF file with a PanSTARRS reference image indicating the location of the candidate, as well as the science, reference, and difference image stamps. An example finding chart can be seen in Figure 13. This service is used in the ALeRCE explorer (see Section 5.2.1).

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Python API Client. We provide a Python client for easier access to the previous API services. It can be installed via pip and is documented at https://alerce.readthedocs.io/en/latest/. You can find examples of how to use the client in the use-case notebooks.

An alert is originated when a significant flux is detected at some location of a difference image between a science and a reference image. In the ZTF alert stream, the difference and reference fluxes are reported for every alert. The science flux is not reported, but it can be recovered from the difference and reference images. The difference flux is reported by its absolute magnitude, m_diff, and sign, sgn, and the reference flux is reported by the PSF photometry magnitude, m_ref, of the closest source in the reference with associated errors, distance, and shape parameters. This leads to three types of cases: (1) the closest source in the reference coincides with the location of the alert, and it is unresolved; (2) the closest source in the reference coincides with the location of the difference image alert, but it is resolved; and (3) the closest source does not coincide with the position of the difference alert. In case (1), the science flux can be recovered exactly; in case (2), it can be recovered plus a constant that depends on how much contamination from an extended source occurs in the reference; and in case (3), one needs to assume that the science flux is equal to the difference flux. These cases are typically represented by variable stars (1), AGNs (2), or transients (3). Since it is not possible to know a priori which correction should be applied to each object, e.g., it is difficult to distinguish an AGN from a nuclear transient until the flux evolution can be observed, we report both the corrected photometry, which is useful for variable stars and AGNs, and the uncorrected photometry, which is useful for transients.

If the reference source is resolved, its reported flux contains two components: a variable/compact component, which is normally the object of study, and a static/extended component, which is difficult to separate using only the ZTF photometry. Because of the convolution done during the image difference process, the extended component should not contribute to the difference flux. Then, we note the following relations:

$$\begin{eqnarray}&&{f}_{\mathrm{ref}}={f}_{\mathrm{ref}}^{\mathrm{ext}}+{f}_{\mathrm{ref}}^{\mathrm{var}},\end{eqnarray} \tag{ A1 }$$

$$\begin{eqnarray}&&{f}_{\mathrm{sci}}={f}_{\mathrm{sci}}^{\mathrm{ext}}+{f}_{\mathrm{sci}}^{\mathrm{var}},\end{eqnarray} \tag{ A2 }$$

$$\begin{eqnarray}&&\mathrm{sgn}{f}_{\mathrm{diff}}={f}_{\mathrm{sci}}^{\mathrm{var}}-{f}_{\mathrm{ref}}^{\mathrm{var}},\end{eqnarray} \tag{ A3 }$$

where f_ref is the reference flux, f_sci is the science flux, $\mathrm{sgn}$ is the sign, f_diff is the absolute value of the difference flux, ${f}_{\mathrm{ref}}^{\mathrm{ext}}$ is the contribution from the extended component in the reference image, ${f}_{\mathrm{ref}}^{\mathrm{var}}$ is the contribution of the variable component in the reference image, ${f}_{\mathrm{sci}}^{\mathrm{ext}}$ is the contribution from the extended component in the science image, and ${f}_{\mathrm{sci}}^{\mathrm{var}}$ is the contribution of the variable component in the science image. Note that the contribution of the extended component can vary between the reference and science images due to seeing effects, which can create an artificial source of variability. The scientifically relevant component for variability studies is the flux of the compact component, but it is difficult to separate it from the extended component. The second-best alternative is to recover the flux of the compact component plus a constant contribution from the extended component. For this, we can define an effective science flux, ${\hat{f}}_{\mathrm{sci}}$,

$$\begin{eqnarray}&&{\hat{f}}_{\mathrm{sci}}\equiv {f}_{\mathrm{ref}}^{\mathrm{ext}}+{f}_{\mathrm{sci}}^{\mathrm{var}},\end{eqnarray} \tag{ A4 }$$

$$\begin{eqnarray}&&={f}_{\mathrm{ref}}+\mathrm{sgn}\,{f}_{\mathrm{diff}},\end{eqnarray} \tag{ A5 }$$

which considers the same contribution of the extended component at all times. If the reference image changes, we can introduce a new effective science flux, ${\hat{f}}_{\mathrm{ref},0}$, that considers the contribution from the extended component from the first reference image used to generate alerts,

$$\begin{eqnarray}&&{\hat{f}}_{\mathrm{sci},0}={f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}+{f}_{\mathrm{sci}}^{\mathrm{var}},\end{eqnarray} \tag{ A6 }$$

$$\begin{eqnarray}&&={\hat{f}}_{\mathrm{sci}}+\left({f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}-{f}_{\mathrm{ref}}^{\mathrm{ext}}\right),\end{eqnarray} \tag{ A7 }$$

where ${f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}$ is the (unknown) contribution from the extended component from the first reference image. Note that the expected value from the second term is zero.

The computation of the errors of the science flux must take into account the relation between the difference and reference fluxes, which are correlated. We can estimate the variance of the effective science flux, ${\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}]$, starting from Equation (A5) and using Equations (A1) and (A3):

$$\begin{eqnarray}&&{\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}]={\mathbb{V}}[{f}_{\mathrm{ref}}+\mathrm{sign}\,{f}_{\mathrm{diff}}]\end{eqnarray} \tag{ A8 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{f}_{\mathrm{ref}}]+{\mathbb{V}}[{f}_{\mathrm{diff}}]+2\,\mathrm{Cov}[{f}_{\mathrm{ref}},\mathrm{sign}\,{f}_{\mathrm{diff}}]\end{eqnarray} \tag{ A9 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{f}_{\mathrm{ref}}]+{\mathbb{V}}[{f}_{\mathrm{diff}}]+2\,\mathrm{Cov}[{f}_{\mathrm{ref}}^{\mathrm{ext}}+{f}_{\mathrm{ref}}^{\mathrm{var}},{f}_{\mathrm{sci}}^{\mathrm{var}}-{f}_{\mathrm{ref}}^{\mathrm{var}}]\end{eqnarray} \tag{ A10 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{f}_{\mathrm{ref}}]+{\mathbb{V}}[{f}_{\mathrm{diff}}]-2\,{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}].\end{eqnarray} \tag{ A11 }$$

Note that the variance due to sky emission is contained in the first two terms of Equation (A16). One can also include additional terms in Equation (A10) to reflect the contribution of the sky, but because these terms are not correlated, they have no additional contribution in the covariance. We can expand Equation (A11) to get the following:

$$\begin{eqnarray}&&{\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}]={\mathbb{V}}[{f}_{\mathrm{ref}}]+{\mathbb{V}}[{f}_{\mathrm{diff}}]-2\,{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]\end{eqnarray} \tag{ A12 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}+{f}_{\mathrm{ref}}^{\mathrm{var}}]+{\mathbb{V}}[{f}_{\mathrm{diff}}]-2\,{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]\end{eqnarray} \tag{ A13 }$$

$$\begin{eqnarray}\begin{array}{rcl} & = & {\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]+2\,\mathrm{Cov}[{f}_{\mathrm{ref}}^{\mathrm{ext}},{f}_{\mathrm{ref}}^{\mathrm{var}}]\\ & & +{\mathbb{V}}[{f}_{\mathrm{diff}}]-2\,{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]\end{array}\end{eqnarray} \tag{ A14 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]+{\mathbb{V}}[{f}_{\mathrm{diff}}]-2\,{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]\end{eqnarray} \tag{ A15 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{f}_{\mathrm{diff}}]-{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}],\end{eqnarray} \tag{ A16 }$$

and, in the case of a change in the reference image, using Equations (A7), (A16), and (A4):

$$\begin{eqnarray}&&{\mathbb{V}}[{\hat{f}}_{\mathrm{sci},0}]={\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}+({f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}-{f}_{\mathrm{ref}}^{\mathrm{ext}})]\end{eqnarray} \tag{ A17 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}]+{\mathbb{V}}[{f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}]-2\,\mathrm{Cov}[{\hat{f}}_{\mathrm{sci}},{f}_{\mathrm{ref}}^{\mathrm{ext}}]\end{eqnarray} \tag{ A18 }$$

$$\begin{eqnarray}\begin{array}{rcl} & = & {\mathbb{V}}[{f}_{\mathrm{diff}}]-{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}]+{\mathbb{V}}[{f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}]\\ & & -2\,\mathrm{Cov}[{f}_{\mathrm{ref}}^{\mathrm{ext}}+{f}_{\mathrm{sci}}^{\mathrm{var}},{f}_{\mathrm{ref}}^{\mathrm{ext}}]\end{array}\end{eqnarray} \tag{ A19 }$$

$$\begin{eqnarray}&&={\mathbb{V}}[{f}_{\mathrm{diff}}]-{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]+{\mathbb{V}}[{f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}].\end{eqnarray} \tag{ A20 }$$

To summarize, we show Equations (A5), (A7), (A16), and (A20):

$$\begin{eqnarray*}\begin{array}{rcl}{\hat{f}}_{\mathrm{sci}} & = & {f}_{\mathrm{ref}}+\mathrm{sgn}{f}_{\mathrm{diff}}\\ {\hat{f}}_{\mathrm{sci},0} & = & {\hat{f}}_{\mathrm{sci}}+({f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}-{f}_{\mathrm{ref}}^{\mathrm{ext}})\\ {\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}] & = & {\mathbb{V}}[{f}_{\mathrm{diff}}]-{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{ext}}]\\ {\mathbb{V}}[{\hat{f}}_{\mathrm{sci},0}] & = & {\mathbb{V}}[{f}_{\mathrm{diff}}]-{\mathbb{V}}[{f}_{\mathrm{ref}}^{\mathrm{var}}]+{\mathbb{V}}[{f}_{\mathrm{ref},\ 0}^{\mathrm{ext}}].\end{array}\end{eqnarray*}$$

A problem with these formulae is that neither the variable nor the extended components are known. However, they led us to consider the following cases.

• 1.  
  The contribution from the extended component is negligible in all reference images:

  $$\begin{eqnarray*}&&{f}_{\mathrm{ref}}^{\mathrm{ext}}=0\end{eqnarray*}$$

  $$\begin{eqnarray*}&&\Rightarrow \end{eqnarray*}$$

  $$\begin{eqnarray}&&{\hat{f}}_{\mathrm{sci},0}={\hat{f}}_{\mathrm{sci}}={f}_{\mathrm{ref}}+\mathrm{sgn}\,{f}_{\mathrm{diff}},\end{eqnarray} \tag{ A21 }$$

  $$\begin{eqnarray}&&{\mathbb{V}}[{\hat{f}}_{\mathrm{sci},0}]={\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}]={\mathbb{V}}[{f}_{\mathrm{diff}}]-{\mathbb{V}}[{f}_{\mathrm{ref}}].\end{eqnarray} \tag{ A22 }$$
• 2.  
  The contribution from the extended component is similar in all reference images, and its contribution is similar to that from the variable component:

  $$\begin{eqnarray*}{f}_{\mathrm{ref},0}^{\mathrm{ext}}={f}_{\mathrm{ref}}^{\mathrm{ext}}\,\&\,{f}_{\mathrm{ref}}^{\mathrm{var}}={f}_{\mathrm{ref}}^{\mathrm{ext}}\end{eqnarray*}$$

  $$\begin{eqnarray*}&&\Rightarrow \end{eqnarray*}$$

  $$\begin{eqnarray}&&{\hat{f}}_{\mathrm{sci},0}={\hat{f}}_{\mathrm{sci}}={f}_{\mathrm{ref}}+\mathrm{sgn}\,{f}_{\mathrm{diff}},\end{eqnarray} \tag{ A23 }$$

  $$\begin{eqnarray}&&{\mathbb{V}}[{\hat{f}}_{\mathrm{sci},0}]={\mathbb{V}}[{\hat{f}}_{\mathrm{sci}}]={\mathbb{V}}[{f}_{\mathrm{diff}}].\end{eqnarray} \tag{ A24 }$$
• 3.  
  The contribution from the extended component is similar in all reference images, and its contribution is dominant over the variable component:

  $$\begin{eqnarray*}{f}_{\mathrm{ref},0}^{\mathrm{ext}}={f}_{\mathrm{ref}}^{\mathrm{ext}}\ \ \&\ \ {f}_{\mathrm{ref}}^{\mathrm{var}}=0\end{eqnarray*}$$

  $$\begin{eqnarray*}&&\Rightarrow \end{eqnarray*}$$

  $$\begin{eqnarray}&&{\hat{f}}_{\mathrm{sci},0}={\hat{f}}_{\mathrm{sci}}={f}_{\mathrm{ref}}+\mathrm{sgn}\,{f}_{\mathrm{diff}},\end{eqnarray} \tag{ A25 }$$

  $$\begin{eqnarray}&&{\mathbb{V}}[{\hat{f}}_{\mathrm{sci},0}]={\mathbb{V}}[{\hat{f}}_{{sci}}]={\mathbb{V}}[{f}_{\mathrm{diff}}]+{\mathbb{V}}[{f}_{\mathrm{ref}}].\end{eqnarray} \tag{ A26 }$$

A visual inspection of variable starlight curves confirms that Equation (A22) is a better approximation in the case where there is no contribution from an extended component. In the case of AGNs, we have found that Equation (A24) appears to be a better reflection of the measurement errors, which is consistent with having a similar contribution from the extended and variable components. In the case of transients, the extended component dominates the flux in the reference, but for these cases, the scientifically relevant flux is the difference flux and its error. For this reason, we report the difference flux with its error, as well as the effective science flux with the errors (after a conversion of the fluxes to magnitudes) from Equations (A22) and (A24) for every object where it is possible to correct the photometry, letting the users decide which flux and error to use for their particular science.

The corrected photometry magnitude results from adding/subtracting the fluxes from the reference and difference in the same unit system and then converting to magnitudes. We can compute ${\hat{f}}_{\mathrm{sci}}$ by transforming the reference and difference magnitudes using the zero-points of the science image,

$$\begin{eqnarray}\begin{array}{rcl}{\hat{f}}_{\mathrm{sci}} & = & {f}_{\mathrm{ref}}+\mathrm{sgn}\,{f}_{\mathrm{diff}}={10}^{\tfrac{{\mathrm{ZP}}_{\mathrm{sci}}-{m}_{\mathrm{ref}}}{2.5}}\\ & & +\mathrm{sgn}\,{10}^{\tfrac{{\mathrm{ZP}}_{\mathrm{sci}}-{m}_{\mathrm{diff}}}{2.5}},\end{array}\end{eqnarray} \tag{ A27 }$$

where ZP_sci is the zero-point of the science image. This implies that the effective science magnitude, ${\hat{m}}_{\mathrm{sci}}$, will be

$$\begin{eqnarray}\begin{array}{rcl}{\hat{m}}_{\mathrm{sci}} & = & -2.5\mathrm{log}{f}_{\mathrm{sci}}+{\mathrm{ZP}}_{\mathrm{sci}}\\ & = & -2.5\mathrm{log}\left({10}^{\tfrac{{\mathrm{ZP}}_{\mathrm{sci}}-{m}_{\mathrm{ref}}}{2.5}}+\mathrm{sgn}\,{10}^{\tfrac{{\mathrm{ZP}}_{\mathrm{sci}}-{m}_{\mathrm{diff}}}{2.5}}\right)+{\mathrm{ZP}}_{\mathrm{sci}}\\ & = & -2.5\mathrm{log}\left({10}^{-\tfrac{{m}_{\mathrm{ref}}}{2.5}}+\mathrm{sgn}\,{10}^{-\tfrac{{m}_{\mathrm{diff}}}{2.5}}\right).\end{array}\end{eqnarray} \tag{ A28 }$$

Finally, we show the reported errors for Equations (A22) and (A24),

$$\begin{eqnarray}&&\delta {\hat{m}}_{\mathrm{sci}}=\displaystyle \frac{{\left({10}^{-0.8{m}_{\mathrm{diff}}}\delta {m}_{\mathrm{diff}}^{2}-{10}^{-0.8{m}_{\mathrm{ref}}}\delta {m}_{\mathrm{ref}}^{2}\right)}^{0.5}}{{10}^{-0.4{m}_{\mathrm{ref}}}+\mathrm{sgn}\,{10}^{-0.4{m}_{\mathrm{diff}}}},\end{eqnarray} \tag{ A29 }$$

to be used when there is no significant contribution from an extended component, or

$$\begin{eqnarray}&&\delta {\hat{m}}_{\mathrm{sci}}=\displaystyle \frac{{10}^{-0.4{m}_{\mathrm{diff}}}\delta {m}_{\mathrm{diff}}}{{10}^{-0.4{m}_{\mathrm{ref}}}+\mathrm{sgn}\,{10}^{-0.4{m}_{\mathrm{diff}}}},\end{eqnarray} \tag{ A30 }$$

to be used when there is a contribution from an extended component assumed to be similar to the variable component.

Table 4 provides the list of telescopes that were used in preparing Figure 1, along with their names and a relevant accompanying reference.

Tables 5, 6, and 7 refer to a number of studies in which light curves were used to perform ML-based classification of variable and transient sources. Tables 5 and 6 both refer to studies in which only persistent variable star classes were used; the former refers to papers published between 2017 and 2019, whereas the latter includes studies that appeared in print before 2017. Table 7, in turn, refers to those studies in which only transient sources were considered. These three tables have the same structure, with the reference given in the first column, an acronym for the source of the data given in the second column (with keys provided in Tables 8 and 9 for empirical and synthetic data, respectively), the number of classes considered shown in the third column, and the fourth column displaying acronyms representing the actual classes that were considered in each case. These acronyms, along with the classes that they are intended to represent, are laid out in Tables 10–14.

In the case of Tables 10 and 11, the pulsating variable star classes are shown. Table 10 includes pulsating stars in the upper and lower main sequence, Cepheids, RR Lyrae, blue subdwarfs, and compact (WD) pulsators. Table 11, in turn, includes red giant and supergiant pulsators.

Table 12 presents a number of additional stellar variability classes, including eclipsing, eruptive, cataclysmic, and rotational variables. Additional classes that are shown in this table include microlensing events, R CrB stars, Be stars, and X-ray binaries, among others.

Primarily extragalactic variable sources are shown in Tables 13 and 14. In the case of Table 13, the variability is typically related to the presence of SMBHs, as in the case of AGNs and QSOs. Table 14, in turn, primarily includes a variety of SN classes, although a few transient events of non-SN origin, such as TDEs and kilonovae, are also included.

We emphasize that the classes and associated taxonomies that are implied by Tables 5–14 do not reflect our own choices but rather are simply a summary of what has been used in the ML literature to date. In particular, the reader should be aware that the list of classes as given suffers from several shortcomings, such as being incomplete, containing redundant entries, and including classes that may not be sufficiently well defined. Still, our best effort to interpret what the different authors have intended to express in each case is reflected in these tables, with definitions given following, among others, the General Catalog of Variable Stars (GCVS; Kholopov et al. 1998), the Variable Star Index (Watson et al. 2006), and the broad overview of stellar variability classes presented in Catelan & Smith (2015). In the future, as the ALeRCE project matures, we will work toward producing and refining our own taxonomy, which we will perfect along the way as we enter the LSST era.