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This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab…
Spiking neural networks (SNNs) receive widespread attention because of their low-power hardware characteristic and brain-like signal response mechanism, but currently, the performance of SNNs is still behind Artificial Neural Networks…
Selective attention helps us focus on task-relevant aspects in the constant flood of our sensory input. This constraint in our perception allows us to robustly generalize under distractions and to new compositions of perceivable concepts.…
Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools…
The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…
Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are…
Shor's r-algorithm (Shor, Zhurbenko (1971), Shor (1979)) with space stretching in the direction of difference of two adjacent subgradients is a competitive method of nonsmooth optimization. However, the original r-algorithm is designed to…
The Bayesian statistical framework provides a systematic approach to enhance the regularization model by incorporating prior information about the desired solution. For the Bayesian linear inverse problems with Gaussian noise and Gaussian…
We propose a new ensemble prediction method, Random Subset Averaging (RSA), tailored for settings with many covariates, particularly in the presence of strong correlations. RSA constructs candidate models via binomial random subset strategy…
In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…
We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…
Attention-based Transformers have revolutionized natural language processing (NLP) and shown strong performance in computer vision (CV) tasks. However, as the input sequence varies, the computational bottlenecks in Transformer models…
This paper presents a factor graph formulation and particle-based sum-product algorithm (SPA) for robust sequential localization in multipath-prone environments. The proposed algorithm jointly performs data association, sequential…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
In this paper, we propose a StochAstic Recursive grAdient algoritHm (SARAH), as well as its practical variant SARAH+, as a novel approach to the finite-sum minimization problems. Different from the vanilla SGD and other modern stochastic…
We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…
We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…
Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…