Related papers: Peres-Style Recursive Algorithms
Efficiently distributing secret keys over long distances remains a critical challenge in the development of quantum networks. "First-generation" quantum repeater chains distribute entanglement by executing protocols composed of…
We present a rejection method based on recursive covering of the probability density function with equal tiles. The concept works for any probability density function that is pointwise computable or representable by tabular data. By the…
We present practical algorithms for generating universal cycles uniformly at random. In particular, we consider universal cycles for shorthand permutations, subsets and multiset permutations, weak orders, and orientable sequences.…
The k-Tree algorithm [Wagner 02] is a non-trivial algorithm for the average-case k-SUM problem that has found widespread use in cryptanalysis. Its input consists of k lists, each containing n integers from a range of size m. Wagner's…
We consider restricted Boltzmann machines with a binary visible layer and a Gaussian hidden layer trained by an unlabelled dataset composed of noisy realizations of a single ground pattern. We develop a statistical mechanics framework to…
Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric…
Sampling from circular distributions is a fundamental task in directional statistics. A key challenge in acceptance-rejection methods lies in selecting an efficient envelope density, as poor choices can lead to low acceptance rates and…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
Binary neural networks (BNN) have been studied extensively since they run dramatically faster at lower memory and power consumption than floating-point networks, thanks to the efficiency of bit operations. However, contemporary BNNs whose…
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is…
A random-key genetic algorithm is an evolutionary metaheuristic for discrete and global optimization. Each solution is encoded as a vector of N random keys, where a random key is a real number randomly generated in the continuous interval…
A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very…
When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are…
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for…
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…
There has been significant progress in Bayesian inference based on sparsity-inducing (e.g., spike-and-slab and horseshoe-type) priors for high-dimensional regression models. The resulting posteriors, however, in general do not possess…