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Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy,…
The Progressive-X algorithm, Prog-X in short, is proposed for geometric multi-model fitting. The method interleaves sampling and consolidation of the current data interpretation via repetitive hypothesis proposal, fast rejection, and…
Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…
Inference-time scaling has emerged as a major approach for improving reasoning capabilities, and has been increasingly applied to diffusion models. However, existing inference-time scaling methods for diffusion models typically rely on…
In implicit collaborative filtering, hard negative mining techniques are developed to accelerate and enhance the recommendation model learning. However, the inadvertent selection of false negatives remains a major concern in hard negative…
We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…
Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…
Accurate prediction of continuous properties is essential to many scientific and engineering tasks. Although deep-learning regressors excel with abundant labels, their accuracy deteriorates in data-scarce regimes. We introduce RankRefine, a…
Reliably characterizing the full conditional distribution of a multivariate response variable given a set of covariates is crucial for trustworthy decision-making. However, misspecified or miscalibrated multivariate models may yield a poor…
Predictive posterior densities (PPDs) are of interest in approximate Bayesian inference. Typically, these are estimated by simple Monte Carlo (MC) averages using samples from the approximate posterior. We observe that the signal-to-noise…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
We present Random Partition Relaxation (RPR), a method for strong quantization of neural networks weight to binary (+1/-1) and ternary (+1/0/-1) values. Starting from a pre-trained model, we quantize the weights and then relax random…
We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…
Prompt-based learning's efficacy across numerous natural language processing tasks has led to its integration into dense passage retrieval. Prior research has mainly focused on enhancing the semantic understanding of pre-trained language…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
Computational models have become a powerful tool in the quantitative sciences to understand the behaviour of complex systems that evolve in time. However, they often contain a potentially large number of free parameters whose values cannot…
Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…
Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and…