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We consider the scenario of supervised learning in Deep Learning (DL) networks, and exploit the arbitrariness of choice in the Riemannian metric relative to which the gradient descent flow can be defined (a general fact of differential…

Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.…

Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…

Multi-label ranking maps instances to a ranked set of predicted labels from multiple possible classes. The ranking approach for multi-label learning problems received attention for its success in multi-label classification, with one of the…

Stream mining poses unique challenges to machine learning: predictive models are required to be scalable, incrementally trainable, must remain bounded in size (even when the data stream is arbitrarily long), and be nonparametric in order to…

Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating…

Despite the remarkable success of deep learning in pattern recognition, deep network models face the problem of training a large number of parameters. In this paper, we propose and evaluate a novel multi-path wavelet neural network…

Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

Optimization of hyper-parameters in reinforcement learning (RL) algorithms is a key task, because they determine how the agent will learn its policy by interacting with its environment, and thus what data is gathered. In this work, an…

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…

Decentralized learning networks aim to synthesize a single network inference from a set of raw inferences provided by multiple participants. To determine the combined inference, these networks must adopt a mapping from historical…

Despite the recent success of stochastic gradient descent in deep learning, it is often difficult to train a deep neural network with an inappropriate choice of its initial parameters. Even if training is successful, it has been known that…

Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…

This paper addresses distributed parameter estimation in randomized one-hidden-layer neural networks. A group of agents sequentially receive measurements of an unknown parameter that is only partially observable to them. In this paper, we…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function…

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…

Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the…