In this paper we present a deployed image recognition system used in a large scale commerce search engine, which we call MSURU. It is designed to process product images uploaded daily to Facebook Marketplace. Social commerce is a growing area within Facebook and understanding visual representations of product content is important for search and recommendation applications on Marketplace. In this paper, we present techniques we used to develop efficient large-scale image classifiers using weakly supervised search log data. We perform extensive evaluation of presented techniques, explain practical experience of developing large-scale classification systems and discuss challenges we faced. Our system, MSURU out-performed current state of the art system developed at Facebook [23] by 16% in e-commerce domain. MSURU is deployed to production with significant improvements in search success rate and active interactions on Facebook Marketplace.

Much of the past work on mining and modeling networks has focused on understanding the observed properties of single example graphs. However, in many real-life applications it is important to characterize the structure of populations of graphs. In this work, we analyze the distributional properties of probabilistic generative graph models (PGGMs) for network populations. PGGMs are statistical methods that model the network distribution and match common characteristics of real-world networks. Specifically, we show that most PGGMs cannot reflect the natural variability in graph properties observed across multiple networks because their edge generation process assumes independence among edges. Then, we propose the mixed Kronecker Product Graph Model (mKPGM), a scalable generalization of KPGMs that uses tied parameters to increase the variability of the sampled networks, while preserving the edge probabilities in expectation. We compare mKPGM to several other graph models. The results show that learned mKPGMs accurately represent the characteristics of real-world networks, while also effectively capturing the natural variability in network structure.

The recent interest in modeling complex networks has fueled the development of generative graph models, such as Kronecker Product Graph Model (KPGM) and mixed KPGM (mKPGM). The Kronecker family of models are appealing because of their elegant fractal structure, as well as their ability to capture important network characteristics such as degree, diameter, and (in the case of mKPGM) clustering and population variance. In addition, scalable sampling algorithms for KPGMs made the analysis of large-scale, sparse networks feasible for the first time. In this work, we show that the scalable sampling methods, in contrast to prior belief, do not in fact sample from the underlying KPGM distribution and often result in sampling graphs that are very unlikely. To address this issue, we develop a new representation that exploits the structure of Kronecker models and facilitates the development of novel grouped sampling methods that are provably correct. In this paper, we outline efficient algorithms to sample from mKPGMs and KPGMs based on these ideas. Notably, our mKPGM algorithm is the first available scalable sampling method for this model and our KPGM algorithm is both faster and more accurate than previous scalable methods. We conduct both theoretical analysis and empirical evaluation to demonstrate the strengths of our algorithms and show that we can sample a network with 75 million edges in 87 seconds on a single processor.

There has recently been a great deal of work focused on developing statistical models of graph structure---with the goal of modeling probability distributions over graphs from which new, similar graphs can be generated by sampling from the estimated distributions. Although current graph models can capture several important characteristics of social network graphs (e.g., degree, path lengths), many of them do not generate graphs with sufficient variation to reflect the natural variability in real world graph domains. One exception is the mixed Kronecker Product Graph Model (mKPGM), a generalization of the Kronecker Product Graph Model, which uses parameter tying to capture variance in the underlying distribution [10]. The enhanced representation of mKPGMs enables them to match both the mean graph statistics and their spread as observed in real network populations, but unfortunately to date, the only method to estimate mKPGMs involves an exhaustive search over the parameters.

We propose a new algorithm for independent component and independent subspace analysis problems. This algorithm uses a contrast based on the Schweizer-Wolff measure of pairwise dependence (Schweizer & Wolff, 1981), a non-parametric measure computed on pairwise ranks of the variables. Our algorithm frequently outperforms state of the art ICA methods in the normal setting, is significantly more robust to outliers in the mixed signals, and performs well even in the presence of noise. Our method can also be used to solve independent subspace analysis (ISA) problems by grouping signals recovered by ICA methods. We provide an extensive empirical evaluation using simulated, sound, and image data.

Finite mixtures of tree-structured distributions have been shown to be efficient and effective in modeling multivariate distributions. Using Dirichlet processes, we extend this approach to allow countably many tree-structured mixture components. The resulting Bayesian framework allows us to deal with the problem of selecting the number of mixture components by computing the posterior distribution over the number of components and integrating out the components by Bayesian model averaging. We apply the proposed framework to identify the number and the properties of predominant precipitation patterns in historical archives of climate data.

We utilize the ensemble of trees framework, a tractable mixture over super- exponential number of tree-structured distributions [1], to develop a new model for multivariate density estimation. The model is based on a construction of tree- structured copulas – multivariate distributions with uniform on [0, 1] marginals. By averaging over all possible tree structures, the new model can approximate distributions with complex variable dependencies. We propose an EM algorithm to estimate the parameters for these tree-averaged models for both the real-valued and the categorical case. Based on the tree-averaged framework, we propose a new model for joint precipitation amounts data on networks of rain stations.

We describe the application of probabilistic model-based learning to the problem of automatically identifying classes of galaxies, based on both morphological and pixel intensity characteristics. The EM algorithm can be used to learn how to spatially orient a set of galaxies so that they are geometrically aligned. We augment this “ordering-model” with a mixture model on objects, and demonstrate how classes of galaxies can be learned in an unsupervised manner using a two-level EM algorithm. The resulting models provide highly accurate classi£cation of galaxies in cross-validation experiments. 1 Introduction and Background The £eld of astronomy is increasingly data-driven as new observing instruments permit the rapid collection of massive archives of sky image data. In this paper we investigate the problem of identifying bent-double radio galaxies in the FIRST (Faint Images of the Radio Sky at Twenty-cm) Survey data set [1]. FIRST produces large numbers of radio images of the deep sky using the Very Large Array at the National Radio Astronomy Observatory. It is scheduled to cover more that 10,000 square degrees of the northern and southern caps (skies). Of particular scienti£c interest to astronomers is the identi£cation and cataloging of sky objects with a “bent-double” morphology, indicating clusters of galaxies ([8], see Figure 1). Due to the very large number of observed deep-sky radio sources, (on the order of 106 so far) it is infeasible for the astronomers to label all of them manually. The data from the FIRST Survey (http://sundog.stsci.edu/) is available in both raw image format and in the form of a catalog of features that have been automatically derived from the raw images by an image analysis program [8]. Each entry corresponds to a single detectable “blob” of bright intensity relative to the sky background: these entries are called Figure 1: 4 examples of radio-source galaxy images. The two on the left are labelled as “bent-doubles” and the two on the right are not. The con£gurations on the left have more “bend” and symmetry than the two non-bent-doubles on the right. components. The “blob” of intensities for each component is £tted with an ellipse. The ellipses and intensities for each component are described by a set of estimated features such as sky position of the centers (RA (right ascension) and Dec (declination)), peak density ¤ux and integrated ¤ux, root mean square noise in pixel intensities, lengths of the major and minor axes, and the position angle of the major axis of the ellipse counterclockwise from the north. The goal is to £nd sets of components that are spatially close and that resemble a bent-double. In the results in this paper we focus on candidate sets of components that have been detected by an existing spatial clustering algorithm [3] where each set consists of three components from the catalog (three ellipses). As of the year 2000, the catalog contained over 15,000 three-component con£gurations and over 600,000 con£gurations total. The set which we use to build and evaluate our models consists of a total of 128 examples of bent-double galaxies and 22 examples of non-bent-double con£gurations. A con£guration is labelled as a bent-double if two out of three astronomers agree to label it as such. Note that the visual identi£cation process is the bottleneck in the process since it requires signi£cant time and effort from the scientists, and is subjective and error-prone, motivating the creation of automated methods for identifying bent-doubles. Three-component bent-double con£gurations typically consist of a center or “core” com- ponent and two other side components called “lobes”. Previous work on automated classi£- cation of three-component candidate sets has focused on the use of decision-tree classi£ers using a variety of geometric and image intensity features [3]. One of the limitations of the decision-tree approach is its relative in¤exibility in handling uncertainty about the object being classi£ed, e.g., the identi£cation of which of the three components should be treated as the core of a candidate object. A bigger limitation is the £xed size of the feature vec- tor. A primary motivation for the development of a probabilistic approach is to provide a framework that can handle uncertainties in a ¤exible coherent manner. 2 Learning to Match Orderings using the EM Algorithm We denote a three-component con£guration by C = (c 1; c2; c3), where the ci’s are the components (or “blobs”) described in the previous section. Each component cx is repre- sented as a feature vector, where the speci£c features will be de£ned later. Our approach focuses on building a probabilistic model for bent-doubles: p (C) = p (c1; c2; c3), the like- lihood of the observed ci under a bent-double model where we implicitly condition (for now) on the class “bent-double.” By looking at examples of bent-double galaxies and by talking to the scientists study- ing them, we have been able to establish a number of potentially useful characteristics of the components, the primary one being geometric symmetry. In bent-doubles, two of the components will look close to being mirror images of one another with respect to a line through the third component. We will call mirror-image components lobe compo-