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We present Matrix Krasulina, an algorithm for online k-PCA, by generalizing the classic Krasulina’s method (Krasulina, 1969) from vector to matrix case. We show, both theoretically and empirically, that the algorithm naturally adapts to data low-rankness and converges exponentially fast to the ground-truth principal subspace. Notably, our result suggests that despite various recent efforts to accelerate

We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same product recommendation repeatedly) or infeasible (e.g. compute job scheduling on machines). We show that with prior knowledge of the rewards and delays of all the arms,

We might hope that when faced with unexpected inputs, well-designed software systems would fire off warnings. Machine learning (ML) systems, however, which depend strongly on properties of their inputs (e.g. the i.i.d. assumption), tend to fail silently. This paper explores the problem of building ML systems that fail loudly, investigating methods for detecting dataset shift, identifying exemplars that

We propose a constraint-based causal feature selection method for identifying causes of a given target variable, selecting from a set of candidate variables, while there can also be hidden variables acting as common causes with the target. We prove that if we observe a cause for each candidate cause, then a single conditional independence test with one conditioning variable is sufficient to decide whether

VP

We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We design dynamic pricing algorithms

In the last decade, it has been shown that many hard AI tasks, especially in NLP, can be naturally modeled as extreme classification problems leading to improved precision. However, such models are prohibitively expensive to train due to the memory blow-up in the last layer. For example, a reasonable softmax layer for the dataset of interest in this paper can easily reach well beyond 100 billion parameters

This paper studies the problem of adaptively sampling from K distributions (arms) in order to identify the largest gap between any two adjacent means. We call this the MaxGap-bandit problem. This problem arises naturally in approximate ranking, noisy sorting, outlier detection, and top-arm identification in bandits. The key novelty of the MaxGap bandit problem is that it aims to adaptively determine the

Algorithms that fuse multiple input sources benefit from both complementary and shared information. Shared information may provide robustness against faulty or noisy inputs, which is indispensable for safety-critical applications like self-driving cars. We investigate learning fusion algorithms that are robust against noise added to a single source. We first demonstrate that robustness against single source

Communication bottleneck has been identified as a significant issue in distributed optimization of large-scale learning models. Recently, several approaches to mitigate this problem have been proposed, including different forms of gradient compression or computing local models and mixing them iteratively. In this paper, we propose Qsparse-local-SGD algorithm, which combines aggressive sparsification with

Understanding the principles of causal inference in the visual system has a long history at least since the seminal studies by Albert Michotte. Many cognitive and machine learning scientists believe that intelligent behavior requires agents to possess causal models of the world. Recent ML algorithms exploit the dependence structure of additive noise terms for inferring causal structures from observational

Applied Scientist

Large-scale distributed training of neural networks is often limited by network bandwidth, wherein the communication time overwhelms the local computation time. Motivated by the success of sketching methods in sub-linear/streaming algorithms, we introduce SKETCHEDSGD, an algorithm for carrying out distributed SGD by communicating sketches instead of full gradients. We show that SKETCHED-SGD has favorable

We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed PrimalDual Block Frank-Wolfe algorithm reduces the per-iteration cost while maintaining linear convergence rate. The per iteration cost of our method depends on the structural complexity of

We study the problem of inverting a deep generative model with ReLU activations. Inversion corresponds to finding a latent code vector that explains observed measurements as much as possible. In most prior works this is performed by attempting to solve a non-convex optimization problem involving the generator. In this paper we obtain several novel theoretical results for the inversion problem. We show that

Manager, Applied Science

Principal, Applied Scientist

With the advent of conversational assistants, like Amazon Alexa, Google Now, etc., dialogue systems are gaining a lot of traction, especially in industrial setting. These systems typically consist of Spoken Language understanding component which, in turn, consists of two tasks - Intent Classification (IC) and Slot Labeling (SL)...