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Graphical models have found widespread applications in many areas of modern statistics and machine learning. Iterative Proportional Fitting (IPF) and its variants have become the default method for undirected graphical model estimation, and…

Iterative feature space optimization involves systematically evaluating and adjusting the feature space to improve downstream task performance. However, existing works suffer from three key limitations:1) overlooking differences among data…

Although multi-view unsupervised feature selection (MUFS) is an effective technology for reducing dimensionality in machine learning, existing methods cannot directly deal with incomplete multi-view data where some samples are missing in…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging…

Unbiased assessment of the predictivity of models learnt by supervised machine-learning methods requires knowledge of the learned function over a reserved test set (not used by the learning algorithm). The quality of the assessment depends,…

We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of…

Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By…

Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…

Consensus maximisation (MaxCon), which is widely used for robust fitting in computer vision, aims to find the largest subset of data that fits the model within some tolerance level. In this paper, we outline the connection between MaxCon…

Due to their cost, experiments for inertial confinement fusion (ICF) heavily rely on numerical simulations to guide design. As simulation technology progresses, so too can the fidelity of models used to plan for new experiments. However,…

Exact inference in Bayesian networks is intractable and has an exponential dependence on the size of the largest clique in the corresponding clique tree (CT), necessitating approximations. Factor based methods to bound clique sizes are more…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

Frequent Subgraph Mining (FSM) is the process of identifying common subgraph patterns that surpass a predefined frequency threshold. While FSM is widely applicable in fields like bioinformatics, chemical analysis, and social network anomaly…

Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…

In this work, we develop a multi-fidelity Bayesian experimental design framework to efficiently quantify the extreme-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. The…

Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…

Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework…

This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…

In this paper, we present a new adaptive feature scaling scheme for ultrahigh-dimensional feature selection on Big Data. To solve this problem effectively, we first reformulate it as a convex semi-infinite programming (SIP) problem and then…