We address the problem of identifying the structure of an undirected graph from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable indirect relationships generated by a diffusion process on the graph. Our approach …
Is it possible to learn the laws of music theory directly from raw sheet music in the same human-interpretable form as a music theory textbook? How little prior knowledge needs to be encoded to do so? We consider these and similar questions in other topical domains, in developing a general …
Accurate and efficient reduced-order models are essential to understand, predict, estimate, and control complex, multiscale, and nonlinear dynamical systems. These models should ideally be generalizable, interpretable, and based on limited training data. This work develops a general framework to discover the governing equations underlying a dynamical system simply from data …
Data collection and sharing are pervasive aspects of modern society. This process can either be voluntary, as in the case of a person taking a facial image to unlock his/her phone, or inciden-tal, such as traf?c cameras collecting videos on pedestrians. An undesirable side effect of these processes is that …
Traditional multistage stochastic optimization assumes the underlying probability distribution is known. However, in practice, the probability distribution is often not known or cannot be accurately approximated. One way to address such distributional ambiguity is to use distributionally robust optimization (DRO), which minimizes the worst-case expected cost with respect to a …
Privacy is the problem of ensuring limited leakage of information about sensitive features while sharing information (utility) about non-private features to legitimate data users. Even as differential privacy has emerged as a strong desideratum for privacy, there is also an equally strong need for context-aware utility-guaranteeing approaches in many data …
Learning a policy using only observational data is challenging because the distribution of states it induces at execution time may differ from the distribution observed during training. In this work, we propose to train a policy while explicitly penalising the mismatch between these two distributions over a fixed time horizon. …
We present a generalization of the collaborative filtering algorithm for the task of tensor estimation, i.e. estimating a low-rank 3-order n-by-n-by-n tensor from noisy observations of randomly chosen entries in the sparse regime. Not only does the algorithm have desirable computational properties, it also provably achieves sample complexity that (nearly) …
Adaptive experimental design (AED), or active learning, leverages already-collected data to guide future measurements, in a closed loop, to collect the most informative data for the learning problem at hand. In both theory and practice, AED can extract considerably richer insights than any measurement plan fixed in advance, using the …
Recently, the surge of interest in deep neural learning has dramatically improved image and signal processing, which has fueled breakthroughs in many domains such as drug discovery, genomics, and automatic translation. These advances have been further applied to scientific computing and, in particular, to electronic structure computations. In this case, …