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We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
We study the problem of computationally and label efficient PAC active learning $d$-dimensional halfspaces with Tsybakov Noise~\citep{tsybakov2004optimal} under structured unlabeled data distributions. Inspired…
Deep neural networks for time series must capture complex temporal patterns, to effectively represent dynamic data. Self- and semi-supervised learning methods show promising results in pre-training large models, which -- when finetuned for…
Deep metric learning is essential for visual recognition. The widely used pair-wise (or triplet) based loss objectives cannot make full use of semantical information in training samples or give enough attention to those hard samples during…
In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied…
In this paper, we apply the Monte Carlo stochastic optimization (MOST) proposed by the authors to a deep learning of XOR gate and verify its effectiveness. Deep machine learning based on neural networks is one of the most important keywords…
In many fields where the main goal is to produce sequential forecasts for decision making problems, the good understanding of the contemporaneous relations among different series is crucial for the estimation of the covariance matrix. In…
As a basic component of SE(3)-equivariant deep feature learning, steerable convolution has recently demonstrated its advantages for 3D semantic analysis. The advantages are, however, brought by expensive computations on dense, volumetric…
We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…
Deep learning has led to state-of-the-art results for many medical imaging tasks, such as segmentation of different anatomical structures. With the increased numbers of deep learning publications and openly available code, the approach to…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the…
In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure…
Many existing branch and bound algorithms for multiobjective optimization problems require a significant computational cost to approximate the entire Pareto optimal solution set. In this paper, we propose a new branch and bound algorithm…
Predicting human trajectories is a challenging task due to the complexity of pedestrian behavior, which is influenced by external factors such as the scene's topology and interactions with other pedestrians. A special challenge arises from…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse…