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In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…
We present a novel approach to feature labeling using gradient descent in token-space. While existing methods typically use language models to generate hypotheses about feature meanings, our method directly optimizes label representations…
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…
Traditionally, neural networks are parameterized using optimization procedures such as stochastic gradient descent, RMSProp and ADAM. These procedures tend to drive the parameters of the network toward a local minimum. In this article, we…
Optimizing embedded systems, where the optimization of one depends on the state of another, is a formidable computational and algorithmic challenge, that is ubiquitous in real world systems. We study flow networks, where bilevel…
Optical marker-based motion capture is a vital tool in applications such as motion and behavioural analysis, animation, and biomechanics. Labelling, that is, assigning optical markers to the pre-defined positions on the body is a time…
This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…
We show that the sensor self-localization problem can be cast as a static parameter estimation problem for Hidden Markov Models and we implement fully decentralized versions of the Recursive Maximum Likelihood and on-line…
Designing a multi-layer optical system with designated optical characteristics is an inverse design problem in which the resulting design is determined by several discrete and continuous parameters. In particular, we consider three design…
Curriculum learning can improve neural network training by guiding the optimization to desirable optima. We propose a novel curriculum learning approach for image classification that adapts the loss function by changing the label…
In this paper we analyze a budgeted learning setting, in which the learner can only choose and observe a small subset of the attributes of each training example. We develop efficient algorithms for ridge and lasso linear regression, which…
The vast majority of work in self-supervised learning, both theoretical and empirical (though mostly the latter), have largely focused on recovering good features for downstream tasks, with the definition of "good" often being intricately…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
Inherent in virtually every iterative machine learning algorithm is the problem of hyper-parameter tuning, which includes three major design parameters: (a) the complexity of the model, e.g., the number of neurons in a neural network, (b)…
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…
For several decades, image restoration remains an active research topic in low-level computer vision and hence new approaches are constantly emerging. However, many recently proposed algorithms achieve state-of-the-art performance only at…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
We present an approach to learn a dense pixel-wise labeling from image-level tags. Each image-level tag imposes constraints on the output labeling of a Convolutional Neural Network (CNN) classifier. We propose Constrained CNN (CCNN), a…