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Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…
Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
The rapid proliferation of artificial intelligence (AI) models and methods presents growing challenges for research software engineers and researchers who must select, integrate, and maintain appropriate models within complex research…
Given a family of feasible subsets of a ground set, the packing problem is to find a largest subfamily of pairwise disjoint family members. Non-approximability renders heuristics attractive viable options, while efficient methods with…
Sampling one or more effective solutions from large search spaces is a recurring idea in machine learning, and sequential optimization has become a popular solution. Typical examples include data summarization, sample mining for predictive…
A fundamental open question in self-supervised learning (SSL) is the explicit characterization of the optimal geometry of the learned representations. Recently, LeJEPA identified isotropic Gaussian embeddings as optimal for minimizing…
Many statistical learning problems have recently been shown to be amenable to Semi-Definite Programming (SDP), with community detection and clustering in Gaussian mixture models as the most striking instances [javanmard et al., 2016]. Given…
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while…
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…
In the classic circle packing problem, one asks whether a given set of circles can be packed into a given container. Packing problems like this have been shown to be $\mathsf{NP}$-hard. In this paper, we present new sufficient conditions…
Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Though quite challenging, leveraging large-scale unlabeled or partially labeled images in a cost-effective way has increasingly attracted interests for its great importance to computer vision. To tackle this problem, many Active Learning…
For a distribution function $F$ on $\mathbb{R}^d$ and a point $q\in \mathbb{R}^d$, the \emph{spherical depth} $\SphD(q;F)$ is defined to be the probability that a point $q$ is contained inside a random closed hyper-ball obtained from a pair…
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…
Semantic segmentation is one of the core tasks in the field of computer vision, and its goal is to accurately classify each pixel in an image. The traditional Unet model achieves efficient feature extraction and fusion through an…
This paper introduces key machine learning operations that allow the realization of robust, joint 6D pose estimation of multiple instances of objects either densely packed or in unstructured piles from RGB-D data. The first objective is to…
Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…