相关论文: Optimal dictionary for least squares representatio…
The top word list, i.e., the top-M words with highest marginal probability in a given topic, is the standard topic representation in topic models. Most of recent automatical topic labeling algorithms and popular topic quality metrics are…
This paper presents a partial solution to a component of the problem of lexical choice: choosing the synonym most typical, or expected, in context. We apply a new statistical approach to representing the context of a word through lexical…
The three-dimensional cylindrical regression problem is a problem of finding a cylinder best fitting a group of points in three-dimensional Euclidean space. The words best fitting are usually understood in the sense of the minimum root mean…
The matrix $A:\mathbb{R}^n \to \mathbb{R}^m$ is $(\delta,k)$-regular if for any $k$-sparse vector $x$, $$ \left| \|Ax\|_2^2-\|x\|_2^2\right| \leq \delta \sqrt{k} \|x\|_2^2. $$ We show that if $A$ is $(\delta,k)$-regular for $1 \leq k \leq…
We design optimal $2 \times N$ ($2 <N$) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by…
Superlatives are used to single out elements with a maximal/minimal property. Semantically, superlatives perform a set comparison: something (or some things) has the min/max property out of a set. As such, superlatives provide an ideal…
Recently, great attention was intended toward overcomplete dictionaries and the sparse representations they can provide. In a wide variety of signal processing problems, sparsity serves a crucial property leading to high performance.…
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a…
Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a…
Convolutional sparse representations are a form of sparse representation with a structured, translation invariant dictionary. Most convolutional dictionary learning algorithms to date operate in batch mode, requiring simultaneous access to…
Strings are a natural representation of biological data such as DNA, RNA and protein sequences. The problem of finding a string that summarizes a set of sequences has direct application in relative compression algorithms for genome and…
Semidefinite programming is based on optimization of linear functionals over convex sets defined by linear matrix inequalities, namely, inequalities of the form $$L_A(X)=I-A_1X_1-\dots-A_g X_g\succeq0.$$ Here the $X_j$ are real numbers and…
Distributional semantics models derive word space from linguistic items in context. Meaning is obtained by defining a distance measure between vectors corresponding to lexical entities. Such vectors present several problems. In this paper…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…
In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show…
This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
Word embeddings have been shown to be useful across state-of-the-art systems in many natural language processing tasks, ranging from question answering systems to dependency parsing. (Herbelot and Vecchi, 2015) explored word embeddings and…