Related papers: Asymptotic elimination of partially continuous agg…
Given a graphical degree sequence ${\bf d}=(d_1,\ldots, d_n)$, let $G(n, {\bf d})$ denote a uniformly random graph on vertex set $[n]$ where vertex $ i$ has degree $d_i$ for every $1\le i\le n$. We give upper and lower bounds on the joint…
Simulation studies are indispensable for evaluating statistical methods and ubiquitous in statistical research. The most common simulation approach is parametric simulation, where the data-generating mechanism (DGM) corresponds to a…
We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key…
Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging…
Current approaches for modeling discrete-valued outcomes associated with spatially-dependent areal units incur computational and theoretical challenges, especially in the Bayesian setting when full posterior inference is desired. As an…
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run…
In this research monograph, we deal with a very general asymptotic representation for statistics named GRI expressed in the functional empirical process, both one-dimensional and multidimensional, and another call residual empirical…
A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method…
Stochastic gradient descent (SGD) algorithm is an effective learning strategy to build a latent factor analysis (LFA) model on a high-dimensional and incomplete (HDI) matrix. A particle swarm optimization (PSO) algorithm is commonly adopted…
Large scale Gaussian process (GP) regression is infeasible for larger data sets due to cubic scaling of flops and quadratic storage involved in working with covariance matrices. Remedies in recent literature focus on divide-and-conquer,…
We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\Delta$-AI). Our approach is based on the observation that when the sampling of variables in a…
The availability of multi-omics data has revolutionized the life sciences by creating avenues for integrated system-level approaches. Data integration links the information across datasets to better understand the underlying biological…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time…
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…
Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…
We present a generic algorithm for learning and approximate inference with an intuitive epistemic interpretation: iteratively focus on a subset of the model and resolve inconsistencies using the parameters under control. This framework,…