We consider multistage adaptive sensing of signals and spectra where the components of interest are sparse. The advantage of adaptation in this context is the ability to focus more of the sensing budget on regions where signal components exist, thereby improving the signal-to-noise ratio. A dynamic programming formulation is derived …
Problems of packing shapes with maximal density, possibly into a container of restricted size, are classical in discrete mathematics. We describe here the problem of packing ellipsoids of given (but varying) dimensions into a finite container, in a way that minimizes the maximum overlap between adjacent ellipsoids. A bilevel optimization …
his talk will focus on progress towards a more “unified” theory for complex networks motivated by biology and technology, and involving several elements: hard limits on achievable robust performance ( “laws”), the organizing principles that succeed or fail in achieving them (architectures and protocols), the resulting high variability data and …
Kevin: This work provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and those with access to only function evaluations. However, there are situations in which DFO is …
We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this setting, these procedures require that individuals provide a complete ranking of all items, which …
Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient methods for solving such problems, working within a high-dimensional framework that allows the data dimension d to grow with (and …
Sparse Principal Component Analysis (SPCA) is a remarkably useful tool for practitioners who had been relying on ad-hoc thresholding methods. Our analysis aims at providing a a framework to test whether the data at hand indeed contains a sparse principal component. More precisely we propose an optimal test procedure to …
The large-scale gathering and storage of personal data is raising new questions about the regulation of privacy. On the technology side, there has been a flurry of recent work on new models for privacy risk and protection. One such model is differential privacy, which quantifies the risk to an individual’s …
In many real-world classification problems, the labels of training examples are randomly corrupted. That is, the set of training examples for each class is contaminated by examples of the other class. Existing approaches to this problem assume that the two classes are separable, that the label noise is independent of …
Many inferential tasks, such as analyzing the functional connectivity of the brain via coactivation patterns or capturing the changing correlations amongst a set of assets for portfolio optimization, rely on modeling a covariance matrix whose elements evolve as a function of time. A number of multivariate heteroscedastic time series models …