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Molecular sciences address a wide range of problems involving molecules of different types and sizes and their complexes. Recently, geometric deep learning, especially Graph Neural Networks, has shown promising performance in molecular…

Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…

Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…

Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…

Motivation: In a predictive modeling setting, if sufficient details of the system behavior are known, one can build and use a simulation for making predictions. When sufficient system details are not known, one typically turns to machine…

Protein-ligand scoring is an important step in a structure-based drug design pipeline. Selecting a correct binding pose and predicting the binding affinity of a protein-ligand complex enables effective virtual screening. Machine learning…

The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate…

Existing works based on molecular knowledge neglect the 3D geometric structure of molecules and fail to learn the high-dimensional information of medications, leading to structural confusion. Additionally, it does not extract key…

The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this work, we present a novel analysis tool to handle discrete…

The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…

We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…

We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…

Structure-based virtual screening must address a combinatorial explosion arising from up to 10^60 drug-like molecules, multiple conformations of proteins and ligands, and all possible spatial translations and rotations of ligands within the…

Machine learning solutions are very popular in the field of chemoinformatics, where they have numerous applications, such as novel drug discovery or molecular property prediction. Molecular fingerprints are algorithms commonly used for…

We provide a methodology for learning sparse statistical models that use as features all possible multiplicative interactions among an underlying atomic set of features. While the resulting optimization problems are exponentially sized, our…

Molecular docking is a crucial step in drug development, which enables the virtual screening of compound libraries to identify potential ligands that target proteins of interest. However, the computational complexity of traditional docking…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…

The design of neural architectures for structured objects is typically guided by experimental insights rather than a formal process. In this work, we appeal to kernels over combinatorial structures, such as sequences and graphs, to derive…