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Fraudulent activities are an expensive problem for many financial institutions, costing billions of dollars to corporations annually. More commonly occurring activities in this regard are credit card frauds. In this context, the credit card…

Depth completion aims to predict a dense depth map from a color image with sparse depth measurements. Although deep learning methods have achieved state-of-the-art (SOTA), effectively handling the sparse and irregular nature of input depth…

Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple…

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…

Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…

Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by…

In this work, we propose variations of a Gaussian mixture model (GMM) based channel estimator that was recently proven to be asymptotically optimal in the minimum mean square error (MMSE) sense. We account for the need of low computational…

In this paper, we derive a priori error estimates for a class of interior penalty discontinuous Galerkin (DG) methods using immersed finite element (IFE) functions for a classic second-order elliptic interface problem. The error estimation…

General matrix/matrix multiplication (GEMM) is crucial for scientific computing and machine learning. However, the increased scale of the computing platforms raises concerns about hardware and software reliability. In this poster, we…

General Matrix Multiplication (GEMM) is a crucial algorithm for various applications such as machine learning and scientific computing, and an efficient GEMM implementation is essential for the performance of these systems. While…

Estimation of distribution algorithms (EDA) are stochastic optimization algorithms. EDA establishes a probability model to describe the distribution of solution from the perspective of population macroscopically by statistical learning…

We investigate the capabilities and limitations of Gaussian process models by jointly exploring three complementary directions: (i) scalable and statistically efficient inference; (ii) flexible kernels; and (iii) objective functions for…

Developing deep generative models that flexibly incorporate diverse measures of probability distance is an important area of research. Here we develop an unified mathematical framework of f-divergence generative model, f-GM, that…

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

Generalized energy detection (GED) is analytically studied when operates under fast-faded channels and in the presence of generalized noise. For the first time, the McLeish distribution is used to model the underlying noise, which is…

A long-standing belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) -- referred to as standard BO -- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both…