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 …
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, …
Several important families of computational and statistical results in machine learning and randomized algorithms rely on statistical independence of data. The scope of such results include the Johnson-Lindenstrauss Lemma (JLL), the Restricted Isometry Property (RIP), regression models, and stochastic optimization. In this talk, we will discuss a new result on …
Fitting a model to a collection of observations is one of the quintessential questions in statistics. The standard assumption is that the data was generated by a model of a given type (e.g., a mixture model). This simplifying assumption is at best only approximately valid, as real datasets are typically …
A restricted Boltzmann machine (RBM) is a type of undirected graphical model with one hidden and one visible layer of variables, where all variables in one layer are conditionally independent given variables in the other layer. In recent years, RBMs have risen to prominence due to their connection to deep …
We consider the global optimization of nonconvex quadratic programs and mixed-integer quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through perturbations of the quadratic matrix. We investigate the theoretical properties of these quadratic relaxations and show that they are equivalent …