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Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…
Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often…
Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…
It has been believed that stochastic feedforward neural networks (SFNNs) have several advantages beyond deterministic deep neural networks (DNNs): they have more expressive power allowing multi-modal mappings and regularize better due to…
Estimates of the generalization error are proved for a residual neural network with $L$ random Fourier features layers $\bar z_{\ell+1}=\bar z_\ell + \mathrm{Re}\sum_{k=1}^K\bar b_{\ell k}e^{\mathrm{i}\omega_{\ell k}\bar z_\ell}+…
One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…
Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful…
Learning in uncertain, noisy, or adversarial environments is a challenging task for deep neural networks (DNNs). We propose a new theoretically grounded and efficient approach for robust learning that builds upon Bayesian estimation and…
We consider principled alternatives to unsupervised learning in data mining by situating the learning task in the context of the subsequent analysis task. Specifically, we consider a query-answering (hypothesis-testing) task: In the…
Rubinfeld & Vasilyan recently introduced the framework of testable learning as an extension of the classical agnostic model. It relaxes distributional assumptions which are difficult to verify by conditions that can be checked efficiently…
We propose and study a new model for reinforcement learning with rich observations, generalizing contextual bandits to sequential decision making. These models require an agent to take actions based on observations (features) with the goal…
A leading family of algorithms for state estimation in dynamic systems with multiple sub-states is based on particle filters (PFs). PFs often struggle when operating under complex or approximated modelling (necessitating many particles)…
Recent work has shown the surprising power of low-degree sandwiching polynomial approximators in the context of challenging learning settings such as learning with distribution shift, testable learning, and learning with contamination. A…
The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…
Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…
According to a popular viewpoint, neural networks learn from data by first identifying low-dimensional representations, and subsequently fitting the best model in this space. Recent works provide a formalization of this phenomenon when…
Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
This paper presents a new method for solving Fokker-Planck equations (FPE) by learning a neural sampler for the distribution given by the FPE via an adversarial training based on a weak formulation of the FPE where the adjoint operator of…