Related papers: Solving high-dimensional parameter inference: marg…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…
Temporal prediction is inherently uncertain, but representing the ambiguity in natural image sequences is a challenging high-dimensional probabilistic inference problem. For natural scenes, the curse of dimensionality renders explicit…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…
Soft demodulation of received symbols into bit log-likelihood ratios (LLRs) is at the very heart of multiple-input-multiple-output (MIMO) detection. However, the optimal maximum a posteriori (MAP) detector is complicated and infeasible to…
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…
This paper proposes a probabilistic neural network developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of…
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…
The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
We study the problem of propagating the mean and covariance of a general multivariate Gaussian distribution through a deep (residual) neural network using layer-by-layer moment matching. We close a longstanding gap by deriving exact moment…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…