A New Transform for Time-Frequency Analysis

This paper describes how a signal can be written as a weighted sum of certain elementary synthesizing functions, which are the dilated and translated versions of a single parent function. The weighting constants in this sum define a transform of the signal. This is much like Fourier analysis except that a wide choice is permitted in the selection of a set of synthesizing functions. Moreover, the permitted sets of synthesizing functions are not orthogonal. It is shown that the transform described here captures both the frequency content, and the temporal evolution, of a non-stationary signal

Approximate Inference in Continuous Determinantal Point Processes

Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of the defining kernel matrix. Recently, there has been growing interest in using DPPs defined on continuous spaces. While the discrete-DPP sampler extends formally to the continuous case, computationally, the steps required are not tractable in general. In this paper, we present two efficient DPP sampling schemes that apply to a wide range of kernel functions: one based on low rank approximations via Nystrom and random Fourier feature techniques and another based on Gibbs sampling. We demonstrate the utility of continuous DPPs in repulsive mixture modeling and synthesizing human poses spanning activity spaces

A Divide-and-Conquer Approach to Syntax-Guided Synthesis

Program synthesis aims to generate programs automatically from user-provided specifications. One critical research thrust is called Syntax-Guideds Synthesis. In addition to semantic specifications, the user should also provide a syntactic template of the desired program, which helps the synthesizer reduce the search space. The traditional symbolic approaches, such as CounterExample-Guided Inductive Synthesis (CEGIS) framework, does not scale to large search spaces. The goal of this project is to explore a compositional, divide-n-conquer approach that heuristically divides the synthesis task into subtasks and solves them separately. The idea is to decompose the function to be synthesized by creating a set of auxiliary functions. In this way, the whole synthesis task can be reduced to synthesizing the auxiliary functions. The auxiliary functions are of bounded size and hence can be encoded into a logic constraint in linear-integer arithmetic and solved by modern Satisfiability-Modulo-Theories (SMT) solvers. In each iteration of the synthesis algorithm, an auxiliary function is synthesized and added into the syntax for synthesizing other auxiliary functions. The algorithms repeats until a syntax-correct implementation equivalent to the reference implementation is found. Preliminary experimental results show that this approach is promising