The goal of this talk is to give some examples of metrics spaces and to look at properties of different types of maps between them. One class of examples I will talk about are delta hyperbolic spaces. These are spaces that are important in certain areas of pure mathematics but …
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in …
Finding models with a low-dimensional structure, given a number of linear observations much smaller than the ambient dimension, has been well-studied in recent years. Examples of such models are sparse vectors, low-rank matrices, and the sum of sparse and low-rank matrices, among others. In many signal processing and machine learning …
Gautam’s Talk: TItle: Active Learning on Graphs Label prediction on graphs, i.e., the prediction of the labels of the vertices of a given graph using the labels of a subset of vertices, is a problem that commonly occurs in many areas of machine learning and data analysis. In this talk …
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 …