Related papers: Optimal dictionary for least squares representatio…

In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of discrete points or unions of sets; or implicitly defined, as…

The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…

We study the problem of representing a discrete tensor that comes from finite uniform samplings of a multi-dimensional and multiband analog signal. Particularly, we consider two typical cases in which the shape of the subbands is cubic or…

Current distributed representations of words show little resemblance to theories of lexical semantics. The former are dense and uninterpretable, the latter largely based on familiar, discrete classes (e.g., supersenses) and relations (e.g.,…

In the last few years, the notion of optimal polynomial approximant has appeared in the mathematics literature in connection with Hilbert spaces of analytic functions of one or more variables. In the 70s, researchers in engineering and…

Many applications, including natural language processing, sensor networks, collaborative filtering, and federated learning, call for estimating discrete distributions from data collected in batches, some of which may be untrustworthy,…

Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the…

With the rapid development of information technologies, centralized data processing is subject to many limitations, such as computational overheads, communication delays, and data privacy leakage. Decentralized data processing over…

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…

Probabilistic word embeddings have shown effectiveness in capturing notions of generality and entailment, but there is very little work on doing the analogous type of investigation for sentences. In this paper we define probabilistic models…

We study the problem of globally recovering a dictionary from a set of signals via $\ell_1$-minimization. We assume that the signals are generated as i.i.d. random linear combinations of the $K$ atoms from a complete reference dictionary…

Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As…

Word2Vec is the most popular model for word representation and has been widely investigated in literature. However, its noise distribution for negative sampling is decided by empirical trials and the optimality has always been ignored. We…

Dictionary learning is a versatile method to produce an overcomplete set of vectors, called atoms, to represent a given input with only a few atoms. In the literature, it has been used primarily for tasks that explore its powerful…

Mid-level features based on visual dictionaries are today a cornerstone of systems for classification and retrieval of images. Those state-of-the-art representations depend crucially on the choice of a codebook (visual dictionary), which is…

Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically formulate the dictionary learning problem as an optimisation with respect to two variables, i.e., dictionary…

Despite many applications, dimensionality reduction in the $\ell_1$-norm is much less understood than in the Euclidean norm. We give two new oblivious dimensionality reduction techniques for the $\ell_1$-norm which improve exponentially…

Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…

The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied…

A method of {\it topological grammars} is proposed for multidimensional data approximation. For data with complex topology we define a {\it principal cubic complex} of low dimension and given complexity that gives the best approximation for…