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The Virtual Element Method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a Balancing Domain Decomposition…
Anomaly detection using dimensionality reduction has been an essential technique for monitoring multidimensional data. Although deep learning-based methods have been well studied for their remarkable detection performance, their…
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms…
We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions for learners that are empirical risk minimizers (ERM) to be computable, and bound the strong…
We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target…
Vector Symbolic Architecture (VSA) is emerging in machine learning due to its efficiency, but they are hindered by issues of hyperdimensionality and accuracy. As a promising mitigation, the Low-Dimensional Computing (LDC) method…
This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of…
Obtaining accurate solutions to the Schr\"odinger equation is the key challenge in computational quantum chemistry. Deep-learning-based Variational Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms of accuracy,…
Semantic segmentation is a fundamental task in computer vision, which can be considered as a per-pixel classification problem. Recently, although fully convolutional neural network (FCN) based approaches have made remarkable progress in…
In the optimization of dynamic systems, the variables typically have constraints. Such problems can be modeled as a Constrained Markov Decision Process (CMDP). This paper considers the peak Constrained Markov Decision Process (PCMDP), where…
Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. Among all valid confidence sets for…
Explaining the unreasonable effectiveness of deep learning has eluded researchers around the globe. Various authors have described multiple metrics to evaluate the capacity of deep architectures. In this paper, we allude to the radius…
Precision and Recall are fundamental metrics in machine learning tasks where both accurate predictions and comprehensive coverage are essential, such as in multi-label learning, language generation, medical studies, and recommender systems.…
Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk…
Vector-Quantized Variational Autoencoders (VQ-VAE)[1] provide an unsupervised model for learning discrete representations by combining vector quantization and autoencoders. In this paper, we study the use of VQ-VAE for representation…
We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average $L_p$ distance between the learned classifier and the…
In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by Dwork et al. (2006) that ensures that the output of an…
Deep Learning models encode rich semantic information in their hidden representations. However, it remains challenging to understand which parts of this information models actually rely on when making predictions. A promising line of…
Our goal is to learn control policies for robots that provably generalize well to novel environments given a dataset of example environments. The key technical idea behind our approach is to leverage tools from generalization theory in…
Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry,…