Multivariable averaging on sparse sets

Adaptive Approximate Querying of Large Sparse Binary Data Sets via Probabilisti Model Averaging

On Reductions of NP Sets to Sparse Sets

We prove unlikely consequences of the existence of sparse hard sets for P under deterministic as well as one-sided error randomized truth-table reductions. Our main results are as follows. We establish that the existence of a polynomially dense hard set for P under (randomized) logspace bounded truth-table reductions implies that P (R)L, and that the collapse goes down to P (R)NC 1 in case of r...

On Random Reductions from Sparse Sets to Tally Sets

We s h o w that every sparse set S can be many-one reduced to an appropriate tally set T by a polynomial-time, randomized reduction (see formal deenitions below.) Since T is in NP if S is in NP, this result can be used to show that there is a tally set in NP being randomized many-one complete for all sparse sets in NP. This partially answers an open problem posed by Hartmanis and Yesha 6]. In 6...

On Identification of Sparse Multivariable ARX Model: A Sparse Bayesian Learning Approach

Although system identification of complex networks is widely studied, most of the work focuses on modelling the dynamics of the ground truth without exploring the topology because in many applications, the network topology is known as a priori. For instance, in industry since the system is artificial, its topology is fixed and the system dynamics is identified for the purpose of control. Nevert...

Sparse Reconstruction via Bayesian Model Averaging

The problem of accurately representing a real-world signal by a concise list of numbers lies at the heart of signal processing. With bandlimited signals, for example, Nyquist theory tells us that we need to sample at twice the highest frequency. But most signals (e.g., speech, audio, images, video) can be represented much more concisely (i.e., “compressed”) if we take advantage of additional st...