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This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…
A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to $1$. In some cases it is required to represent…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as in other disciplines. In 1971, Sch{\"o}nhage and Strassen designed an algorithm that improved the multiplication time for…
Locally Differentially Private (LDP) Reports are commonly used for collection of statistics and machine learning in the federated setting. In many cases the best known LDP algorithms require sending prohibitively large messages from the…
We present fast and efficient randomized distributed algorithms to find Hamiltonian cycles in random graphs. In particular, we present a randomized distributed algorithm for the $G(n,p)$ random graph model, with number of nodes $n$ and…
Sampling from binary quadratic distributions (BQDs) is a fundamental but challenging problem in discrete optimization and probabilistic inference. Previous work established theoretical guarantees for stochastic localization (SL) in…
The training phases of Deep neural network~(DNN) consumes enormous processing time and energy. Compression techniques utilizing the sparsity of DNNs can effectively accelerate the inference phase of DNNs. However, it can be hardly used in…
Sampling-based motion planning algorithms are widely used in robotics because they are very effective in high-dimensional spaces. However, the success rate and quality of the solutions are determined by an adequate selection of their…
Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in…
Fast secure random number generation is essential for high-speed encrypted communication, and is the backbone of information security. Generation of truly random numbers depends on the intrinsic randomness of the process used and is usually…
We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics.…
In this paper, we study the optimal dividend problem under the continuous time diffusion model with the bounded dividend rate from the Reinforcement Learning (RL) perspective. Unlike the standard literature, our main focus will be on…
In random allocation rules, typically first an optimal fractional point is calculated via solving a linear program. The calculated point represents a fractional assignment of objects or more generally packages of objects to agents. In order…
The Ziggurat Algorithm is a very fast rejection sampling method for generating PseudoRandom Numbers (PRNs) from common statistical distributions. The algorithm divides a distribution into rectangular layers that stack on top of each other…
Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of…
Pseudorandom values are often generated as 64-bit binary words. These random words need to be converted into ranged values without statistical bias. We present an efficient algorithm to generate multiple independent uniformly-random bounded…
Recent byte-level language models (LMs) match the performance of token-level models without relying on subword vocabularies, yet their utility is limited by slow, byte-by-byte autoregressive generation. We address this bottleneck in the…
Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…
Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is…