Related papers: Concentration inequalities for semidefinite least …
Self-supervised learning (SSL) is a scalable way to learn general visual representations since it learns without labels. However, large-scale unlabeled datasets in the wild often have long-tailed label distributions, where we know little…
We consider the problem of certifying lower bounds for real-valued multivariate transcendental functions. The functions we are dealing with are nonlinear and involve semialgebraic operations as well as some transcendental functions like…
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…
We revisit classical connectivity problems in the CONGEST model of distributed computing. By using techniques from fault tolerant network design, we show improved constructions, some of which are even "local" (i.e., with $\widetilde{O}(1)$…
Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on…
Finite-State Dynamics (FSD) is one of the simplest and constrained distributed systems. An FSD is defined by an $n$-node network, with each node maintaining an internal state selected from a finite set. At each time-step, these nodes…
We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…
Federated Learning (FL) is a distributed machine learning framework that trains accurate global models while preserving clients' privacy-sensitive data. However, most FL approaches assume that clients possess labeled data, which is often…
Semi-Supervised Learning (SSL) has become a preferred paradigm in many deep learning tasks, which reduces the need for human labor. Previous studies primarily focus on effectively utilising the labelled and unlabeled data to improve…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe…
The trust-region problem, which minimizes a nonconvex quadratic function over a ball, is a key subproblem in trust-region methods for solving nonlinear optimization problems. It enjoys many attractive properties such as an exact…
In recent years, there has been remarkable progress in the development of so-called certifiable perception methods, which leverage semidefinite, convex relaxations to find global optima of perception problems in robotics. However, many of…
Semi-supervised learning (SSL) has shown great promise in leveraging unlabeled data to improve model performance. While standard SSL assumes uniform data distribution, we consider a more realistic and challenging setting called imbalanced…
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…