相关论文: Optimal dictionary for least squares representatio…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
There are two main approaches to the distributed representation of words: low-dimensional deep learning embeddings and high-dimensional distributional models, in which each dimension corresponds to a context word. In this paper, we combine…
Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…
Minimal-interval semantics associates with each query over a document a set of intervals, called witnesses, that are incomparable with respect to inclusion (i.e., they form an antichain): witnesses define the minimal regions of the document…
We introduce a definition of the volume for a general rectangular matrix, which for square matrices is equivalent to the absolute value of the determinant. We generalize results for square maximum-volume submatrices to the case of…
Finding the best set of gestures to use for a given computer recognition problem is an essential part of optimizing the recognition performance while being mindful to those who may articulate the gestures. An objective function, called the…
Recently, \cite{CRT,DonohoPol} theoretically analyzed the success of a polynomial $\ell_1$-optimization algorithm in solving an under-determined system of linear equations. In a large dimensional and statistical context \cite{CRT,DonohoPol}…
Given a set of points of interest, a volumetric spanner is a subset of the points using which all the points can be expressed using "small" coefficients (measured in an appropriate norm). Formally, given a set of vectors $X = \{v_1, v_2,…
This paper provides an insight into the possibility of how to find ontologies most relevant to scientific texts using artificial neural networks. The basic idea of the presented approach is to select a representative paragraph from a source…
We study the optimal linear prediction of a random function that takes values in an infinite dimensional Hilbert space. We begin by characterizing the mean square prediction error (MSPE) associated with a linear predictor and discussing the…
We consider the decomposition of a signal over an overcomplete set of vectors. Minimization of the $\ell^1$-norm of the coefficient vector can often retrieve the sparsest solution (so-called "$\ell^1/\ell^0$-equivalence"), a generally…
This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…
Distributed representations of words have been shown to capture lexical semantics, as demonstrated by their effectiveness in word similarity and analogical relation tasks. But, these tasks only evaluate lexical semantics indirectly. In this…
Separable, or Kronecker product, dictionaries provide natural decompositions for 2D signals, such as images. In this paper, we describe a highly parallelizable algorithm that learns such dictionaries which reaches sparse representations…
This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…
We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that $O (n \log n)$ samples are sufficient to uniquely determine the coefficient matrix.…
Sentences are important semantic units of natural language. A generic, distributional representation of sentences that can capture the latent semantics is beneficial to multiple downstream applications. We observe a simple geometry of…
Distributed representations of words as real-valued vectors in a relatively low-dimensional space aim at extracting syntactic and semantic features from large text corpora. A recently introduced neural network, named word2vec (Mikolov et…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
Word representations are created using analogy context-based statistics and lexical relations on words. Word representations are inputs for the learning models in Natural Language Understanding (NLU) tasks. However, to understand language,…