SimJoint - Simulate Joint Distribution

Simulate multivariate correlated data given nonparametric marginals and their joint structure characterized by a Pearson or Spearman correlation matrix. The simulator engages the problem from a purely computational perspective. It assumes no statistical models such as copulas or parametric distributions, and can approximate the target correlations regardless of theoretical feasibility. The algorithm integrates and advances the Iman-Conover (1982) approach <doi:10.1080/03610918208812265> and the Ruscio-Kaczetow iteration (2008) <doi:10.1080/00273170802285693>. Package functions are carefully implemented in C++ for squeezing computing speed, suitable for large input in a manycore environment. Precision of the approximation and computing speed both substantially outperform various CRAN packages to date. Benchmarks are detailed in function examples. A simple heuristic algorithm is additionally designed to optimize the joint distribution in the post-simulation stage. The heuristic demonstrated good potential of achieving the same level of precision of approximation without the enhanced Iman-Conover-Ruscio-Kaczetow. The package contains a copy of Permuted Congruential Generator.

Last updated 1 years ago

openblascpp

2.00 score 2 scripts 254 downloads

FLSSS - Mining Rigs for Problems in the Subset Sum Family

Specialized solvers for combinatorial optimization problems in the Subset Sum family. The solvers differ from the mainstream in the options of (i) restricting subset size, (ii) bounding subset elements, (iii) mining real-value multisets with predefined subset sum errors, (iv) finding one or more subsets in limited time. A novel algorithm for mining the one-dimensional Subset Sum induced algorithms for the multi-Subset Sum and the multidimensional Subset Sum. The multi-threaded framework for the latter offers exact algorithms to the multidimensional Knapsack and the Generalized Assignment problems. Historical updates include (a) renewed implementation of the multi-Subset Sum, multidimensional Knapsack and Generalized Assignment solvers; (b) availability of bounding solution space in the multidimensional Subset Sum; (c) fundamental data structure and architectural changes for enhanced cache locality and better chance of SIMD vectorization; (d) option of mapping floating-point instance to compressed 64-bit integer instance with user-controlled precision loss, which could yield substantial speedup due to the dimension reduction and efficient compressed integer arithmetic via bit-manipulations; (e) distributed computing infrastructure for multidimensional subset sum; (f) arbitrary-precision zero-margin-of-error multidimensional Subset Sum accelerated by a simplified Bloom filter. The package contains a copy of xxHash from <https://github.com/Cyan4973/xxHash>. Package vignette (<doi:10.48550/arXiv.1612.04484>) detailed a few historical updates. Functions prefixed with 'aux' (auxiliary) are independent implementations of published algorithms for solving optimization problems less relevant to Subset Sum.

Last updated 24 days ago

gmpcpp

1.78 score 1 stars 20 scripts 355 downloads

GMKMcharlie - Unsupervised Gaussian Mixture and Minkowski and Spherical K-Means with Constraints

High performance trainers for parameterizing and clustering weighted data. The Gaussian mixture (GM) module includes the conventional EM (expectation maximization) trainer, the component-wise EM trainer, the minimum-message-length EM trainer by Figueiredo and Jain (2002) <doi:10.1109/34.990138>. These trainers accept additional constraints on mixture weights, covariance eigen ratios and on which mixture components are subject to update. The K-means (KM) module offers clustering with the options of (i) deterministic and stochastic K-means++ initializations, (ii) upper bounds on cluster weights (sizes), (iii) Minkowski distances, (iv) cosine dissimilarity, (v) dense and sparse representation of data input. The package improved the typical implementations of GM and KM algorithms in various aspects. It is carefully crafted in multithreaded C++ for modeling large data for industry use.

Last updated 4 years ago

openblascpp

1.00 score 1 stars 232 downloads