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Computing accurate yet efficient approximations to the solutions of the electronic Schr\"odinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of…

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First,…

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

Second-order methods have the capability of accelerating optimization by using much richer curvature information than first-order methods. However, most are impractical for deep learning, where the number of training parameters is huge. In…

The $k$-principal component analysis ($k$-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications. In statistical settings, the goal of $k$-PCA is to identify a top…

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…

Quadratic assignment problems (QAPs) arise in a wide variety of domains, ranging from operations research to graph theory to computer vision to neuroscience. In the age of big data, graph valued data is becoming more prominent, and with it,…

Cross-correlator plays a significant role in many visual perception tasks, such as object detection and tracking. Beyond the linear cross-correlator, this paper proposes a kernel cross-correlator (KCC) that breaks traditional limitations.…

We provide a general framework for getting expected linear time constant factor approximations (and in many cases FPTASs) to several well-known problems in Computational Geometry, such as $k$-center clustering and farthest nearest neighbor.…

3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…

Pre-trained models are widely used in fine-tuning downstream tasks with linear classifiers optimized by the cross-entropy loss, which might face robustness and stability problems. These problems can be improved by learning representations…

Knowledge graph embedding research has mainly focused on learning continuous representations of entities and relations tailored towards the link prediction problem. Recent results indicate an ever increasing predictive ability of current…

Many applications, such as system identification, classification of time series, direct and inverse problems in partial differential equations, and uncertainty quantification lead to the question of approximation of a non-linear operator…

Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes.…

We propose an end-to-end integrated strategy to produce highly accurate quantum chemistry (QC) synthetic datasets (energies and forces) aimed at deriving Foundation Machine Learning models for molecular simulation. Starting from Density…

Graph learning, or network inference, is a prominent problem in graph signal processing (GSP). GSP generalizes the Fourier transform to non-Euclidean domains, and graph learning is pivotal to applying GSP when these domains are unknown.…

We introduce a quadratically-constrained approximation (QCAC) of the AC optimal power flow (AC-OPF) problem. Unlike existing approximations like the DC-OPF, our model does not rely on typical assumptions such as high reactance-to-resistance…

Kernel-based reinforcement learning (KBRL) stands out among reinforcement learning algorithms for its strong theoretical guarantees. By casting the learning problem as a local kernel approximation, KBRL provides a way of computing a…

Classification is at the core of data-driven prediction and decision-making, representing a fundamental task in supervised machine learning. Recently, several quantum machine learning algorithms that use quantum kernels as a measure of…

Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever…