Related papers: Ambiguity Sparse Processes
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…
This paper proposes a method for modeling event sequences with ambiguous timestamps, a time-discounting convolution. Unlike in ordinary time series, time intervals are not constant, small time-shifts have no significant effect, and…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
In genomics, differential abundance and expression analyses are complicated by the compositional nature of sequence count data, which reflect only relative-not absolute-abundances or expression levels. Many existing methods attempt to…
The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…
Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…
Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a…
There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number…
We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it…
We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The process is a natural extension of a complex-valued autoregressive process, extended to include a widely linear autoregressive term. This…
The theory of sparse stochastic processes offers a broad class of statistical models to study signals. In this framework, signals are represented as realizations of random processes that are solution of linear stochastic differential…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
Model selection in machine learning (ML) is a crucial part of the Bayesian learning procedure. Model choice may impose strong biases on the resulting predictions, which can hinder the performance of methods such as Bayesian neural networks…
Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…
Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…
Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…