Related papers: Minimax Lower Bounds on Dictionary Learning for Te…
There has been an increased interest in multimodal language processing including multimodal dialog, question answering, sentiment analysis, and speech recognition. However, naturally occurring multimodal data is often imperfect as a result…
In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…
In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric…
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…
This paper investigates the learning of 3rd-order tensors representing the semantics of transitive verbs. The meaning representations are part of a type-driven tensor-based semantic framework, from the newly emerging field of compositional…
We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
We study the problem of communicating a distributed correlated memoryless source over a memoryless network, from source nodes to destination nodes, under quadratic distortion constraints. We establish the following two complementary…
We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…
Data tensors of orders 2 and greater are now routinely being generated. These data collections are increasingly huge and growing. Many scientific and medical data tensors are tensor fields (e.g., images, videos, geographic data) in which…
In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
We obtain the minimax rate for a mean location model with a bounded star-shaped set $K \subseteq \mathbb{R}^n$ constraint on the mean, in an adversarially corrupted data setting with Gaussian noise. We assume an unknown fraction $\epsilon…
It has recently been shown that for compressive sensing, significantly fewer measurements may be required if the sparsity assumption is replaced by the assumption the unknown vector lies near the range of a suitably-chosen generative model.…