Related papers: Matrix of Polynomials Model based Polynomial Dicti…

Structured data, which constitutes a significant portion of existing data types, has been a long-standing research topic in the field of machine learning. Various representation learning methods for tabular data have been proposed, ranging…

In this work we approach the task of learning multilingual word representations in an offline manner by fitting a generative latent variable model to a multilingual dictionary. We model equivalent words in different languages as different…

We present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we…

Polymers are widely-studied materials with diverse properties and applications determined by different molecular structures. It is essential to represent these structures clearly and explore the full space of achievable chemical designs.…

In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample…

We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…

Bilingual word embeddings have been widely used to capture the similarity of lexical semantics in different human languages. However, many applications, such as cross-lingual semantic search and question answering, can be largely benefited…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

In the complex plane, the frequency response of a univariate polynomial is the set of values taken by the polynomial when evaluated along the imaginary axis. This is an algebraic curve partitioning the plane into several connected…

We present an analysis tool based on joint matrix factorization for comparing latent representations of multilingual and monolingual models. An alternative to probing, this tool allows us to analyze multiple sets of representations in a…

In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…

Data-driven approaches to automatic drum transcription (ADT) are often limited to a predefined, small vocabulary of percussion instrument classes. Such models cannot recognize out-of-vocabulary classes nor are they able to adapt to…

Many music theoretical constructs (such as scale types, modes, cadences, and chord types) are defined in terms of pitch intervals---relative distances between pitches. Therefore, when computer models are employed in music tasks, it can be…

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…

A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…

The success of deep networks is crucially attributed to their ability to capture latent features within a representation space. In this work, we investigate whether the underlying learned features of a model can be efficiently retrieved…

In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations. Training deep neural…

Multi-channel acoustic signal processing is a well-established and powerful tool to exploit the spatial diversity between a target signal and non-target or noise sources for signal enhancement. However, the textbook solutions for optimal…

We propose an interactive approach to language learning that utilizes linguistic acceptability judgments from an informant (a competent language user) to learn a grammar. Given a grammar formalism and a framework for synthesizing data, our…