Related papers: Structural Analysis of Vector Autoregressive Model…

In this article, we will look at autoencoders. This article covers the mathematics and the fundamental concepts of autoencoders. We will discuss what they are, what the limitations are, the typical use cases, and we will look at some…

We develop a framework for incorporating structured graphical models in the \emph{encoders} of variational autoencoders (VAEs) that allows us to induce interpretable representations through approximate variational inference. This allows us…

The paper develops a general flexible framework for Network Autoregressive Processes (NAR), wherein the response of each node linearly depends on its past values, a prespecified linear combination of neighboring nodes and a set of…

We develop a shape analysis for reasoning about relational properties of data structures. Both the concrete and the abstract domain are represented by hypergraphs. The analysis is parameterized by user-supplied indexed graph grammars to…

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior…

We consider structural vector autoregressions that are identified through stochastic volatility under Bayesian estimation. Three contributions emerge from our exercise. First, we show that a non-centred parameterization of stochastic…

Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…

This paper analyzes the robustness of deep learning models in autonomous driving applications and discusses the practical solutions to address that.

Next-word predictions from autoregressive neural language models show remarkable sensitivity to syntax. This work evaluates the extent to which this behavior arises as a result of a learned ability to maintain implicit representations of…

We introduce a new approach for abstractive text summarization, Topic-Guided Abstractive Summarization, which calibrates long-range dependencies from topic-level features with globally salient content. The idea is to incorporate neural…

In this work we describe and evaluate methods to learn musical embeddings. Each embedding is a vector that represents four contiguous beats of music and is derived from a symbolic representation. We consider autoencoding-based methods…

Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking by special graphs. Signless formulas…

Autoregressive models are a class of generative model that probabilistically predict the next output of a sequence based on previous inputs. The autoregressive sequence is by definition one-dimensional (1D), which is natural for language…

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…

Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorized likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This…

This work introduces a novel approach for the joint selection of model structure and parameter learning for nonlinear dynamical systems identification. Focusing on a specific Recurrent Neural Networks (RNNs) family, i.e., Nonlinear…

We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time…

These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.

For extracting meaningful topics from texts, their structures should be considered properly. In this paper, we aim to analyze structured time-series documents such as a collection of news articles and a series of scientific papers, wherein…