Existing question answering (QA) datasets are no longer challenging to most powerful Large Language Models (LLMs). Traditional QA benchmarks like TriviaQA, NaturalQuestions, ELI5 and HotpotQA mainly study ''known unknowns'' with clear indications of both what information is missing, and how to find it to answer the question. A yet unmet need of the NLP community is a bank of non-factoid, multi-perspective questions involving a great deal of unclear information needs, i.e. ''unknown unknowns''. We claim we can find such questions in search engine logs, which is surprising because most question-intent queries are indeed factoid. Furthermore, recent products like Google's DeepResearch (announced a year after this resource was released publicly) specifically address such queries, retrieving hundreds of documents to synthesize report-style responses. We present Researchy Questions, the world's first, only and largest public dataset of ''Deep Research'' questions filtered from real search engine logs to be non-factoid, ''decompositional'' and multi-perspective. We show that users spend substantial ''effort'' on these questions in terms of signals like clicks and session length. We also show that ''slow thinking'' answering techniques, like decomposition into sub-questions shows benefit over answering directly. We release (at https://huggingface.co/datasets/corbyrosset/researchy_questions) about 100k Researchy Questions with a permissive CDLA-2.0 license, along with click histograms on over 350k Clueweb22 URLs that were clicked for each question.

Distributed graph neural network (GNN) training facilitates learning on massive graphs that surpass the storage and computational capabilities of a single machine. Traditional distributed frameworks strive for performance parity with centralized training by maximally recovering cross-instance node dependencies, relying either on inter-instance communication or periodic fallback to centralized training. However, these processes create overhead and constrain the scalability of the framework. In this work, we propose a streamlined framework for distributed GNN training that eliminates these costly operations, yielding improved scalability, convergence speed, and performance over state-of-the-art approaches. Our framework (1) comprises independent trainers that asynchronously learn local models from locally available parts of the training graph and (2) synchronizes these local models only through periodic (time-based) model aggregation. Contrary to prevailing belief, our theoretical analysis shows that it is not essential to maximize the recovery of cross-instance node dependencies to achieve performance parity with centralized training. Instead, our framework leverages randomized assignment of nodes or super-nodes (i.e., collections of original nodes) to partition the training graph in order to enhance data uniformity and minimize discrepancies in gradient and loss function across instances. Experiments on social and e-commerce networks with up to 1.3 billion edges show that our proposed framework achieves state-of-the-art performance and 2.31 \(\times\) speedup compared to the fastest baseline despite using less training data.

The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper, we aim to alleviate these issues by learning generalizable inductive biases from the nodes’ local subgraph and transfer them for faster learning over new subgraphs with a disjoint set of nodes, edges, and labels in a few-shot setting. We introduce a novel method, Hyperbolic GRAph Meta Learner (H-GRAM), that, for the tasks of node classification and link prediction, learns transferable information from a set of support local subgraphs in the form of hyperbolic meta gradients and label hyperbolic protonets to enable faster learning over a query set of new tasks dealing with disjoint subgraphs. Furthermore, we show that an extension of our meta-learning framework also mitigates the scalability challenges seen in HNNs faced by existing approaches. Our comparative analysis shows that H-GRAM effectively learns and transfers information in multiple challenging few-shot settings compared to other state-of-the-art baselines. Additionally, we demonstrate that, unlike standard HNNs, our approach is able to scale over large graph datasets and improve performance over its Euclidean counterparts.

At E-Commerce stores such as Amazon, eBay, and Taobao, the shopping items and the query words that customers use to search for the items form a bipartite graph that captures search behavior. Such a query-item graph can be used to forecast search trends or improve search results. For example, generating query-item associations, which is equivalent to predicting links in the bipartite graph, can yield recommendations that can customize and improve the user search experience. Although the bipartite shopping graphs are straightforward to model search behavior, they suffer from two challenges: 1) The majority of items are sporadically searched and hence have noisy/sparse query associations, leading to a long-tail distribution. 2) Infrequent queries are more likely to link to popular items, leading to another hurdle known as disassortative mixing.

The large-scale nature of product catalog and the changing demands of customer queries makes product search a challenging problem. The customer queries are ambiguous and implicit. They may be looking for an exact match of their query, or a functional equivalent (i.e., substitute), or an accessory to go with it (i.e., complement). It is important to distinguish these three categories from merely classifying an item for a customer query as relevant or not. This information can help direct the customer and improve search applications to understand the customer mission. In this paper, we formulate search relevance as a multi-class classification problem and propose a graph-based solution to classify a given query-item pair as exact, substitute, complement, or irrelevant (ESCI). The customer engagement (clicks, add-to-cart, and purchases) between query and items serve as a crucial information for this problem. However, existing approaches rely purely on the textual information (such as BERT) and do not sufficiently focus on the structural relationships. Another challenge in including the structural information is the sparsity of such data in some regions. We propose Structure-Aware multilingual LAnguage Model (SALAM), that utilizes a language model along with a graph neural network, to extract region-specific semantics as well as relational information for the classification of query-product pairs. Our model is first pre-trained on a large region-agnostic dataset and behavioral graph data and then fine-tuned on region-specific versions to address the sparsity. We show in our experiments that SALAM significantly outperforms the current matching frameworks on the ESCI classification task in several regions. We also demonstrate the effectiveness of using a two-phased training setup (i.e., pre-training and fine-tuning) in capturing region-specific information. Also, we provide various challenges and solutions for using the model in an industrial setting and outline its contribution to the e-commerce engine.

Recent studies have revealed important properties that are unique to graph datasets such as hierarchies and global structures. This has driven research into hyperbolic space due to their ability to effectively encode the inherent hierarchy present in graph datasets. However, a major bottleneck here is the obscurity of hyperbolic geometry and a better comprehension of its gyrovector operations. In this tutorial, we aim to introduce researchers and practitioners in the data mining community to the hyperbolic equivariants of the Euclidean operations that are necessary to tackle their application to neural networks. We describe the popular hyperbolic variants of GNN architectures and explain their implementation, in contrast to the Euclidean counterparts. Also, we motivate our tutorial through critical analysis of existing applications in the areas of graph mining, knowledge graph reasoning, search, NLP, and computer vision.

Embeddings, low-dimensional vector representation of objects, are fundamental in building modern machine learning systems. In industrial settings, there is usually an embedding team that trains an embedding model to solve intended tasks (e.g., product recommendation). The produced embeddings are then widely consumed by consumer teams to solve their unintended tasks (e.g., fraud detection). However, as the embedding model gets updated and retrained to improve performance on the intended task, the newly-generated embeddings are no longer compatible with the existing consumer models. This means that historical versions of the embeddings can never be retired or all consumer teams have to retrain their models to make them compatible with the latest version of the embeddings, both of which are extremely costly in practice.

Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision making and search under uncertainty. In modern applications however, one is often faced with a tremendously large number of options and even obtaining one observation per option may be too costly rendering traditional pure exploration algorithms ineffective. Fortunately, one often has access to similarity relationships amongst the options that can be leveraged. In this paper, we consider the pure exploration problem in stochastic multi-armed bandits where the similarities between the arms is captured by a graph and the rewards may be represented as a smooth signal on this graph. In particular, we consider the problem of finding the arm with the maximum reward (i.e., the maximizing problem) or one that has sufficiently high reward (i.e., the satisficing problem) under this model. We propose novel algorithms GRUB (GRaph based UcB) and zeta-GRUB for these problems and provide theoretical characterization of their performance which specifically elicits the benefit of the graph side information. We also prove a lower bound on the data requirement that shows a large class of problems where these algorithms are near-optimal. We complement our theory with experimental results that show the benefit of capitalizing on such side information.

Graph Neural Networks (GNNs) have emerged as powerful tools to encode graph-structured data. Due to their broad applications, there is an increasing need to develop tools to explain how GNNs make decisions given graph-structured data. Existing learning-based GNN explanation approaches are task-specific in training and hence suffer from crucial drawbacks. Specifically, they are incapable of producing explanations for a multitask prediction model with a single explainer. They are also unable to provide explanations in cases where the GNN is trained in a self-supervised manner, and the resulting representations are used in future downstream tasks. To address these limitations, we propose a Task-Agnostic GNN Explainer (TAGE) that is independent of downstream models and trained under self-supervision with no knowledge of downstream tasks. TAGE enables the explanation of GNN embedding models with unseen downstream tasks and allows efficient explanation of multitask models. Our extensive experiments show that TAGE can significantly speed up the explanation efficiency by using the same model to explain predictions for multiple downstream tasks while achieving explanation quality as good as or even better than current state-of-the-art GNN explanation approaches.

Product search is a fundamentally challenging problem due to the large-size of product catalogues and the complexity of extracting semantic information from products. In addition to this, the black-box nature of most search systems also hamper a smooth customer experience. Current approaches in this area utilize lexical and semantic product information to match user queries against products. However, these models lack (i) a hierarchical query representation, (ii) a mechanism to detect and capture inter-entity relationships within a query, and (iii) a query composition method specific to e-commerce domain. To address these challenges, in this paper, we propose an AtteNTive Hyperbolic Entity Model (ANTHEM), a novel attention-based product search framework that models query entities as two-vector hyperboloids, learns inter-entity intersections and utilizes attention to unionize individual entities and inter-entity intersections to predict product matches from the search space. ANTHEM utilizes the first and second vector of hyperboloids to determine the query's semantic position and to tune its surrounding search volume, respectively. The attention networks capture the significance of intra-entity and inter-entity intersections to the final query space. Additionally, we provide a mechanism to comprehend ANTHEM and understand the significance of query entities towards the final resultant products. We evaluate the performance of our model on real data collected from popular e-commerce sites. Our experimental study on the offline data demonstrates compelling evidence of ANTHEM's superior performance over state-of-the-art product search methods with an improvement of more than 10% on various metrics. We also demonstrate the quality of ANTHEM's query encoder using a query matching task.

Human labeling is time-consuming and costly. This problem is further exacerbated in extremely imbalanced class label scenarios, such as detecting fraudsters in online websites. Active learning selects the most relevant example for human labelers to improve the model performance at a lower cost. However, existing methods for active learning for graph data often assumes that both data and label distributions are balanced. These assumptions fail in extreme rare-class classification scenarios, such as classifying abusive reviews in an e-commerce website.

Due to intense competition and lack of real estate on the front page of large e-commerce platforms, sellers are sometimes motivated to garner non-genuine signals (clicks, add-to-carts, purchases) on their products, to make them appear more appealing to customers. This hurts customers' trust on the platform, and also hurts genuine sellers who sell their items without looking to game the system. While it is important to find the sellers and the buyers who are colluding to garner these non-genuine signals, doing so is highly nontrivial. Firstly, the set of bad actors in the system is a very small fraction of all the buyers/sellers on the platform. Secondly, bad actors ``hide" with the good ones, making them hard to detect. In this paper, we develop CONGCN, a context aware heterogeneous graph convolutional network to detect bad actors on a large heterogeneous graph. While our method is motivated by abuse detection in e-commerce, the method is applicable to other areas such as computational biology and finance, where large heterogeneous graphs are pervasive, and the amount of labeled data is very limited. We train CONGCN via novel sampling methods, and context aware message passing in a semi-supervised fashion to predict dishonest buyers and sellers in e-commerce. Extensive experiments show that our method is effective, beating several baselines; generalizable to an inductive setting and highly scalable

The recent increase in the size of neural networks has led to a proportional increase in the demands for high-quality human-annotated data. Labeling data is a costly and time-consuming endeavor, and the need for large data is often satiated through creative techniques such as data augmentation, transfer learning, self-supervised learning, active learning, to name a few. Many of these techniques are designed for specific data types such as images, text, and speech. The data in many data-mining applications however is multi-modal in nature, has implicit signals from user-interactions, and involves multiple agents. Given the uniqueness, importance, and growing interest in these problems, we feel that the ACM Conference on Knowledge Discovery and Data Mining (SIGKDD) 2021 is an appropriate venue for running a workshop on Data-efficient Machine Learning. In this proposal, we discuss our vision for this workshop.

Abusive behavior in online retail websites and communities threatens the experience of regular community members. Such behavior often takes place within a complex, dynamic, and large-scale network of users interacting with items. Detecting abuse is challenging due to the scarcity of labeled abuse instances and complexity of combining temporal and network patterns while operating at a massive scale. Previous approaches to dynamic graph modeling either do not scale, do not effectively generalize from a few labeled instances, or compromise performance for scalability. Here we present BiDyn, a general method to detect abusive behavior in dynamic bipartite networks at scale, while generalizing from limited training labels. BiDyn develops an efficient hybrid RNN-GNN architecture trained via a novel stacked ensemble training scheme. We also propose a novel pre-training framework for dynamic graphs that helps to achieve superior performance at scale. Our approach outperforms recent large-scale dynamic graph baselines in an abuse classification task by up to 14% AUROC while requiring 10x less memory per training batch in both open and proprietary datasets.

Logical reasoning over Knowledge Graphs (KGs) is a fundamental technique that can provide an efficient querying mechanism over large and incomplete databases. Current approaches employ spatial geometries such as boxes to learn query representations that encompass the answer entities and model the logical operations of projection and intersection. However, their geometry is restrictive and leads to non-smooth strict boundaries, which further results in ambiguous answer entities. Furthermore, previous works propose transformation tricks to handle unions which results in non-closure and, thus, cannot be chained in a stream. In this paper, we propose a Probabilistic Entity Representation Model (PERM) to encode entities as a Multivariate Gaussian density with mean and covariance parameters to capture its semantic position and smooth decision boundary, respectively. Additionally, we also define the closed logical operations of projection, intersection, and union that can be aggregated using an end-to-end objective function. On the logical query reasoning problem, we demonstrate that the proposed PERM significantly outperforms the state-of-the-art methods on various public benchmark KG datasets on standard evaluation metrics. We also evaluate PERM’s competence on a COVID-19 drug-repurposing case study and show that our proposed work is able to recommend drugs with substantially better F1 than current methods. Finally, we demonstrate the working of our PERM’s query answering process through a low-dimensional visualization of the Gaussian representations.

In e-commerce applications, customers search and discover one or more products using queries. Some of these queries are broad and diverse, with multiple intents. Therefore, relying purely on the anonymized and aggregated customer historical behavioral data is not sufficient to train machine learned models. For example, customers may click and purchase a galaxy charger for a "samsung galaxy s9" query. The item is not an exact match for the customer query. However, it serves as a complement to the original query and may be purchased. To address these potential mismatches from surfacing in search results, e-commerce systems rely on machine learned models trained on human- annotated data. There are two challenges in collecting human annotated data. First, the human annotation process does not scale and it is hard to obtain large volumes of annotations in multiple languages. Second, annotators must query existing systems to obtain samples for auditing, resulting in very few mismatched examples (data skewness) and counterfactual biases. In this talk, we address these challenges using two recent advances in deep learning. To address the data skewness, we generate hard negative examples using positive examples. The key idea here is to generate synthetic data using a Variational Encoder Decoder (VED) architecture. We show how a modified loss function with a novel combiner (to combine VED with the classifier) can avoid policy-based gradients and other heuristics. To address the sparsity of data in less popular languages, we combine data across all languages using language-agnostic representation learning. The side information we use aligns the items across languages in the same latent space. We show that our approaches significantly improve upon state of the art baselines, by over 25% in F1 score for the variational model, and over 20% in F1 score for the multilingual model.

Knowledge Graphs (KGs) are ubiquitous structures for information storage in several real-world applications such as web search, e-commerce, social networks, and biology. Querying KGs remains a foundational and challenging problem due to their size and complexity. Promising approaches to tackle this problem include embedding the KG units (e.g., entities and relations) in a Euclidean space such that the query embedding contains the information relevant to its results. These approaches, however, fail to capture the hierarchical nature and semantic information of the entities present in the graph. Additionally, most of these approaches only utilize multi-hop queries (that can be modeled by simple translation operations) to learn embeddings and ignore more complex operations such as intersection, and union of simpler queries. To tackle such complex operations, in this paper, we formulate KG representation learning as a self-supervised logical query reasoning problem that utilizes translation, intersection and union queries over KGs. We propose Hyperboloid Embeddings (HypE), a novel self-supervised dynamic reasoning framework, that utilizes positive first-order existential queries on a KG to learn representations of its entities and relations as hyperboloids in a Poincaré ball. HypE models the positive first-order queries as geometrical translation, intersection, and union. For the problem of KG reasoning in real-world datasets, the proposed HypE model significantly outperforms the state-of-the art results. We also apply HypE to an anomaly detection task on a popular e-commerce website product taxonomy as well as hierarchically organized web articles and demonstrate significant performance improvements compared to existing baseline methods. Finally, we also visualize the learned HypE embeddings in a Poincaré ball to clearly interpret and comprehend the representation space.

Showing items that do not match search query intent degrades customer experience in ecommerce.These mismatches result from counterfactual biases of the ranking algorithms toward noisy behavioral signals such as clicks and purchases in the search logs.Mitigating the problem requires a large labeled dataset, which is expensive and time-consuming to obtain.In this paper, we develop a deep, endto-end model that learns to effectively classify mismatches and to generate hard mismatched examples to improve the classifier.We train the model end-to-end by introducing a latent variable into the cross-entropy loss that alternates between using the real and generated samples.This not only makes the classifier more robust but also boosts the overall ranking performance.Our model achieves a relative gain compared to baselines by over 26% in F-score, and over 17% in Area Under PR curve.On live search traffic, our model gains significant improvement in multiple countries.

Gradient Boosted Decision Trees (GBDTs) are widely used for building ranking and relevance models in search and recommendation. Considerations such as latency and interpretability dictate the use of as few features as possible to train these models. Feature selection in GBDT models typically involves heuristically ranking the features by importance and selecting the top few, or by per- forming a full backward feature elimination routine. On-the-fly feature selection methods proposed previously scale suboptimally with the number of features, which can be daunt- ing in high dimensional settings. We develop a scalable forward feature selection variant for GBDT, via a novel group testing procedure that works well in high dimensions, and enjoys favorable theoretical performance and computational guarantees. We show via ex- tensive experiments on both public and proprietary datasets that the proposed method offers significant speedups in training time, while being as competitive as existing GBDT methods in terms of model performance metrics. We also extend the method to the multitask setting, allowing the practitioner to select common features across tasks, as well as selecting task-specific features.

In this paper, we consider recommender systems with side information in the form of graphs. Existing collaborative filtering algorithms mainly utilize only immediate neighborhood information and do not efficiently take advantage of deeper neighborhoods beyond 1-2 hops. The main issue with exploiting deeper graph information is the rapidly growing time and space complexity when incorporating information from these neighborhoods. In this paper, we propose using Graph DNA, a novel Deep Neighborhood Aware graph encoding algorithm, for exploiting multi-hop neighborhood information. DNA encoding computes approximate deep neighborhood information in linear time using Bloom filters, and results in a per-node encoding whose dimension is logarithmic in the number of nodes in the graph. It can be used in conjunction with both feature-based and graph-regularization-based collaborative filtering algorithms. Graph DNA has the advantages of being memory and time efficient and providing additional regularization when compared to directly using higher order graph information. We provide theoretical performance bounds for graph DNA encoding, and experimentally show that graph DNA can be used with 4 popular collaborative filtering algorithms to consistently boost their performances with little computational and memory overhead.

Product search forms an indispensable component of any e-commerce service, and helps customers find products of their interest from a large catalog on these websites. When products that are irrelevant to the search query are surfaced, it leads to a poor customer experience, thus reducing user trust and increasing the likelihood of churn. While identifying and removing such results from product search is crucial, doing so is a burdensome task that requires large amounts of human annotated data to train accurate models. This problem is exacerbated when products are cross-listed across countries that speak multiple languages, and customers specify queries in multiple languages and from different cultural contexts. In this work, we propose a novel multi-lingual multi-task learning framework, to jointly train product search models on multiple languages, with limited amount of training data from each language. By aligning the query and product representations from different languages into a language-independent vector space of queries and products, respectively, the proposed model improves the performance over baseline search models in any given language. We evaluate the performance of our model on real data collected from a leading e-commerce service. Our experimental evaluation demonstrates up to 23% relative improvement in the classification F1-score compared to the state-of-the-art baseline models.

E-commerce search engines are the primary means by which customers shop for products online. Each customer query contains multiple facets such as product type, color, brand, etc. A successful search engine retrieves products that are relevant to the query along each of these attributes. However, due to lexical (erroneous title, description, etc.) and behavioral irregularities (clicks or purchases of products that do not belong to the same facet as the query), some mismatched products are often included in search results. These irregularities can be detected using simple binary classifiers like gradient boosted decision trees or logistic regression. Typically, these binary classifiers use strong independence assumptions between the results and ignore structural relationships available in the data, such as the connections between products and queries. In this paper, we use the connections that exist between products and query to identify a special kind of structure we refer to as a micrograph. Further, we make use of Statistical Relational Learning (SRL) to incorporate these micrographs in the data and pose the problem as a structured prediction problem. We refer to this approach as structured mismatch classification (\SMC). In addition, we show that naive addition of structure does not improve the performance of the model and hence introduce a variation of \SMC, strong \SMC~(\SSMC), which improves over the baseline by passing information from high-confidence predictions to lower confidence predictions. In our empirical evaluation we show that our proposed approach outperforms the baseline classification methods by up to 12% in precision. Furthermore, we use quasi-Newton methods to make our method viable for real-time inference in a search engine and show that our approach is up to 150 times faster than existing ADMM-based solvers.

Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of human history. However, traditional techniques such as word representation learning do not adequately capture the evolving language structure and vocabulary. In this paper, we develop a dynamic statistical model to learn time-aware word vector representation. We propose a model that simultaneously learns time-aware embeddings and solves the resulting alignment problem. This model is trained on a crawled NYTimes dataset. Additionally, we develop multiple intuitive evaluation strategies of temporal word embeddings. Our qualitative and quantitative tests indicate that our method not only reliably captures this evolution over time, but also consistently outperforms state-of-the-art temporal embedding approaches on both semantic accuracy and alignment quality.

Online reviews have become an inevitable part of a consumer's decision making process, where the likelihood of purchase not only depends on the product's overall rating, but also on the description of its aspects. Therefore, e-commerce websites such as Amazon and Walmart constantly encourage users to write good quality re- views and categorically summarize different facets of the products. However, despite such attempts, it takes a significant effort to skim through thousands of reviews and look for answers that address the query of consumers. For example, a gamer might be interested in buying a monitor with fast refresh rates and support for Gsync and Freesync technologies, while a photographer might be interested in aspects such as color depth and accuracy. To address these chal- lenges, in this paper, we propose a generative aspect summarization model called APSUM that is capable of providing fine-grained sum- maries of online reviews. To overcome the inherent problem of aspect sparsity, we impose dual constraints: (a) a spike-and-slab prior over the document-topic distribution and (b) a linguistic su- pervision over the word-topic distribution. Using a rigorous set of experiments, we show that the proposed model is capable of out- performing the state-of-the-art aspect summarization model over a variety of datasets and deliver intuitive fine-grained summaries that could simplify the purchase decisions of consumers.

Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning both the feature weights and the nonlinear function that relates features to observations. While methods have been described to learn SIMs in the low dimensional regime, a method that can efficiently learn SIMs in high dimensions, and under general structural assumptions, has not been forthcoming. In this paper, we propose computationally efficient algorithms for SIM inference in high dimensions with structural constraints. Our general approach specializes to sparsity, group sparsity, and low-rank assumptions among others. Experiments show that the proposed method enjoys superior predictive performance when compared to generalized linear models, and achieves results comparable to or better than single layer feedforward neural networks with significantly less computational cost.

Several high-dimensional learning applications require the parameters to satisfy a “group sparsity” constraint, where clusters of coefficients are required to be simultaneously selected or rejected. The group lasso and its variants are common methods to solve problems of this form. Recently, in the standard sparse setting, it has been noted that tighter convex relaxations than the ℓ1norm can be obtained by using other regularizers, leading to better predictive performance. Motivated by these discoveries, we develop the group k-support norm to achieve group sparsity with a better predictive accuracy. We develop an efficient algorithm to solve the resulting optimization problems, and show that our approach outperforms traditional methods for prediction and recovery under group sparsity.

Matrix completion (MC) with additional information has found wide applicability in several machine learning applications. Among algorithms for solving such problems, Inductive Matrix Completion(IMC) has drawn a considerable amount of attention, not only for its well established theoretical guarantees but also for its superior performance in various real-world applications. However, IMC based methods usually place very strong constraints on the quality of the features(side information) to ensure accurate recovery, which might not be met in practice. In this paper, we propose Goal-directed Inductive Matrix Completion(GIMC) to learn a nonlinear mapping of the features so that they satisfy the required properties. A key distinction between GIMC and IMC is that the feature mapping is learnt in a supervised manner, deviating from the traditional approach of unsupervised feature learning followed by model training. We establish the superiority of our method on several popular machine learning applications including multi-label learning, multi-class classification, and semi-supervised clustering.

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard thresholding methods have proven to be extremely efficient, but such methods require NP hard projections when dealing with overlapping groups. In this paper, we show that such NP-hard projections can not only be avoided by appealing to submodular optimization, but such methods come with strong theoretical guarantees even in the presence of poorly conditioned data (i.e. say when two features have correlation $\geq 0.99$), which existing analyses cannot handle. These methods exhibit an interesting computation-accuracy trade-off and can be extended to significantly harder problems such as sparse overlapping groups. Experiments on both real and synthetic data validate our claims and demonstrate that the proposed methods are orders of magnitude faster than other greedy and convex relaxation techniques for learning with group-structured sparsity.

Time series prediction problems are becoming increasingly high-dimensional in modern applications, such as climatology and demand forecasting. For example, in the latter problem, the number of items for which demand needs to be forecast might be as large as 50,000. In addition, the data is generally noisy and full of missing values. Thus, modern applications require methods that are highly scalable, and can deal with noisy data in terms of corruptions or missing values. However, classical time series methods usually fall short of handling these issues. In this paper, we present a temporal regularized matrix factorization (TRMF) framework which supports data-driven temporal learning and forecasting. We develop novel regularization schemes and use scalable matrix factorization methods that are eminently suited for high-dimensional time series data that has many missing values. Our proposed TRMF is highly general, and subsumes many existing approaches for time series analysis. We make interesting connections to graph regularization methods in the context of learning the dependencies in an autoregressive framework. Experimental results show the superiority of TRMF in terms of scalability and prediction quality. In particular, TRMF is two orders of magnitude faster than other methods on a problem of dimension 50,000, and generates better forecasts on real-world datasets such as Wal-mart E-commerce datasets.

Low rank matrix completion plays a fundamental role in collaborative filtering applications, the key idea being that the variables lie in a smaller subspace than the ambient space. Often, additional information about the variables is known, and it is reasonable to assume that incorporating this information will lead to better predictions. We tackle the problem of matrix completion when pairwise relationships among variables are known, via a graph. We formulate and derive a highly efficient, conjugate gradient based alternating minimization scheme that solves optimizations with over 55 million observations up to 2 orders of magnitude faster than state-of-the-art (stochastic) gradient-descent based methods. On the theoretical front, we show that such methods generalize weighted nuclear norm formulations, and derive statistical consistency guarantees. We validate our results on both real and synthetic datasets.

Motivated by the problem of robust factorization of a low-rank tensor, we study the question of sparse and low-rank tensor decomposition. We present an efficient computational algorithm that modifies Leurgans' algoirthm for tensor factorization. Our method relies on a reduction of the problem to sparse and low-rank matrix decomposition via the notion of tensor contraction. We use well-understood convex techniques for solving the reduced matrix sub-problem which then allows us to perform the full decomposition of the tensor. We delineate situations where the problem is recoverable and provide theoretical guarantees for our algorithm. We validate our algorithm with numerical experiments.

In many applications in signal and image processing, communications, and system identification, one aims to recover a signal that has a simple representation in a given basis or frame. Key devices for obtaining such representations are objects called atoms, and functions called atomic norms. These concepts unify the idea of simple representations across several known applications, and motivate extensions to new problem classes of interest. In important special cases, fast and efficient algorithms are available to solve the reconstruction problems, but an approach that works well for the general atomic-norm paradigm has not been forthcoming to date. In this paper, we combine a greedy selection scheme with a backward step that sparsifies the basis by removing less significant elements that were included at earlier iterations. We show that the overall scheme achieves the same convergence rate as the forward greedy scheme alone, provided that backward steps are taken only when they do not degrade the solution quality too badly. Finally, we validate our method by describing applications to three problems of interest.

Multitask learning can be effective when features useful in one task are also useful for other tasks, and the group lasso is a standard method for selecting a common subset of features. In this paper, we are interested in a less restrictive form of multitask learning, wherein (1) the available features can be organized into subsets according to a notion of similarity and (2) features useful in one task are similar, but not necessarily identical, to the features best suited for other tasks. The main contribution of this paper is a new procedure called {\em Sparse Overlapping Sets (SOS) lasso}, a convex optimization that automatically selects similar features for related learning tasks. Error bounds are derived for SOSlasso and its consistency is established for squared error loss. In particular, SOSlasso is motivated by multi-subject fMRI studies in which functional activity is classified using brain voxels as features. Experiments with real and synthetic data demonstrate the advantages of SOSlasso compared to the lasso and group lasso.

Dictionary learning has emerged as a powerful tool for low level image processing tasks such as denoising and inpainting, as well as sparse coding and representation of images. While there has been extensive work on the development of online and offline dictionary learning algorithms to perform the aforementioned tasks, the problem of choosing an appropriate dictionary size is not as widely addressed. In this paper, we introduce a new scheme to reduce and optimize dictionary size in an online setting by synthesizing new atoms from multiple previous ones. We show that this method performs as well as existing offline and online dictionary learning algorithms in terms of representation accuracy while achieving significant speedup in dictionary reconstruction and image encoding times. Our method not only helps in choosing smaller and more representative dictionaries, but also enables learning of more incoherent ones.

Statistical correlations among wavelet transform coefficients of images are commonly represented using graphical models. But in linear inverse problems like compressed sensing, the sensing matrix linearly mixes up these dependencies, making recovery of the transform coefficients difficult. Past work has involved using greedy methods to recover images in a compressed sensing framework. Recently, message passing and group lasso based methods have been shown to perform at least as well as traditional approaches. Group lasso based methods are especially viable, since they provide the guarantees that come along with solving a convex program. Standard sensing matrices are well-suited to the recovery of unstructured sparse signals, but the sparsity patterns of natural images are highly structured. In this paper, we look to exploit the intra-group dependencies among coefficients to design sensing matrices that are better matched to image structure than conventional compressed sensing matrices. We show that the new sensing matrices based on structural prior knowledge yield considerably better results compared to standard sensing matrices.

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees (HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in de-convolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso.