Embed and Project: Discrete Sampling with Universal Hashing

Column Sampling Based Discrete Supervised Hashing

By leveraging semantic (label) information, supervised hashing has demonstrated better accuracy than unsupervised hashing in many real applications. Because the hashing-code learning problem is essentially a discrete optimization problem which is hard to solve, most existing supervised hashing methods try to solve a relaxed continuous optimization problem by dropping the discrete constraints. H...

Constrained Sampling and Counting: Universal Hashing Meets SAT Solving

Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these problems was thoroughly investigated in the 1980s, prior work either did not scale to industrial size instances or gave up correctness guarantees to achieve scal...

Fuzzy Universal Hashing and Approximate Authentication

Hashing with Generalized Nyström Approximation

Hashing, which involves learning binary codes to embed high-dimensional data into a similarity-preserving low-dimensional Hamming space, is often formulated as linear dimensionality reduction followed by binary quantization. Linear dimensionality reduction, based on maximum variance formulation, requires leading eigenvectors of data covariance or graph Laplacian matrix. Computing leading singul...

LDPC Codes for Discrete Integration

Discrete integration over exponentially large combinatorial sets is a key task for approximate probabilistic inference. Ermon et al. recently developed an approximation algorithm for discrete integration with provable guarantees using hashing techniques. These works reduce discrete integration to solving a polynomial number of MAP inference queries for models that include random linear parity c...