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Minimization of the $\ell_{\infty}$ (or maximum) norm subject to a constraint that imposes consistency to an underdetermined system of linear equations finds use in a large number of practical applications, including vector quantization,…

Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless,…

It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…

Deep neural networks (DNNs) with high expressiveness have achieved state-of-the-art performance in many tasks. However, their distributed feature representations are difficult to interpret semantically. In this work, human-interpretable…

Over the past years, distributed semantic representations have proved to be effective and flexible keepers of prior knowledge to be integrated into downstream applications. This survey focuses on the representation of meaning. We start from…

Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation…

The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…

Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

Despite the well-developed cut-edge representation learning for language, most language representation models usually focus on specific level of linguistic unit, which cause great inconvenience when being confronted with handling multiple…

Many signal processing problems--such as analysis, compression, denoising, and reconstruction--can be facilitated by expressing the signal as a linear combination of atoms from a well-chosen dictionary. In this paper, we study possible…

For $0<\delta <1$ a $\delta$-subrepetition in a word is a factor which exponent is less than~2 but is not less than $1+\delta$ (the exponent of the factor is the ratio of the factor length to its minimal period). The $\delta$-subrepetition…

Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an…

Co-occurrence statistics based word embedding techniques have proved to be very useful in extracting the semantic and syntactic representation of words as low dimensional continuous vectors. In this work, we discovered that dictionary…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

We consider the problem of synthesizing programs with numerical constants that optimize a quantitative objective, such as accuracy, over a set of input-output examples. We propose a general framework for optimal synthesis of such programs…

Representation learning aims to extract meaningful lower-dimensional embeddings from data, known as representations. Despite its widespread application, there is no established definition of a ``good'' representation. Typically, the…

The Minimum Description Length (MDL) principle is solidly based on a provably ideal method of inference using Kolmogorov complexity. We test how the theory behaves in practice on a general problem in model selection: that of learning the…

A fully-dynamic dictionary is a data structure for maintaining sets that supports insertions, deletions and membership queries. A filter approximates membership queries with a one-sided error. We present two designs: 1. The first…

The notion of $12$-representable graphs was introduced as a variant of a well-known class of word-representable graphs. Recently, these graphs were shown to be equivalent to the complements of simple-triangle graphs. This indicates that a…