DNA samples crime cases analysed in forensic genetics, frequently contain DNA from multiple contributors. These occur as convolutions of the DNA profiles of the individual contributors to the DNA sample. Thus, in cases where one or more of the contributors were unknown, an objective of interest would be the separation, often called deconvolution, of these unknown profiles. In order to obtain deconvolutions of the unknown DNA profiles, we introduced a multiple population evolutionary algorithm (MEA). We allowed the mutation operator of the MEA to utilise that the fitness is based on a probabilistic model and guide it by using the deviations between the observed and the expected value for every element of the encoded individual. This guided mutation operator (GM) was designed such that the larger the deviation the higher probability of mutation. Furthermore, the GM was inhomogeneous in time, decreasing to a specified lower bound as the number of iterations increased. We analysed 102 two-person DNA mixture samples in varying mixture proportions. The samples were quantified using two different DNA prep. kits: (1) Illumina ForenSeq Panel B (30 samples), and (2) Applied Biosystems Precision ID Globalfiler NGS STR panel (72 samples). The DNA mixtures were deconvoluted by the MEA and compared to the true DNA profiles of the sample. We analysed three scenarios where we assumed: (1) the DNA profile of the major contributor was unknown, (2) DNA profile of the minor was unknown, and (3) both DNA profiles were unknown. Furthermore, we conducted a series of sensitivity experiments on the ForenSeq panel by varying the sub-population size, comparing a completely random homogeneous mutation operator to the guided operator with varying mutation decay rates, and allowing for hill-climbing of the parent population.

Variational Bayesian phylogenetic inference (VBPI) provides a promising general variational framework for efficient estimation of phylogenetic posteriors. However, the current diagonal Lognormal branch length approximation would significantly restrict the quality of the approximating distributions. In this paper, we propose a new type of VBPI, VBPI-NF, as a first step to empower phylogenetic posterior estimation with deep learning techniques. By handling the non-Euclidean branch length space of phylogenetic models with carefully designed permutation equivariant transformations, VBPI-NF uses normalizing flows to provide a rich family of flexible branch length distributions that generalize across different tree topologies. We show that VBPI-NF significantly improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian phylogenetic inference problems. Further investigation also reveals that the structured parameterization in those permutation equivariant transformations can provide additional amortization benefit.

Equation discovery, also known as symbolic regression, is a type of automated modeling that discovers scientific laws, expressed in the form of equations, from observed data and expert knowledge. Deterministic grammars, such as context-free grammars, have been used to limit the search spaces in equation discovery by providing hard constraints that specify which equations to consider and which not. In this paper, we propose the use of probabilistic context-free grammars in the context of equation discovery. Such grammars encode soft constraints on the space of equations, specifying a prior probability distribution on the space of possible equations. We show that probabilistic grammars can be used to elegantly and flexibly formulate the parsimony principle, that favors simpler equations, through probabilities attached to the rules in the grammars. We demonstrate that the use of probabilistic, rather than deterministic grammars, in the context of a Monte-Carlo algorithm for grammar-based equation discovery, leads to more efficient equation discovery. Finally, by specifying prior probability distributions over equation spaces, the foundations are laid for Bayesian approaches to equation discovery.

This article was published as a part of the Data Science Blogathon. In this digital world, spam is the most troublesome challenge that everyone is facing. Sending spam messages to people causes various problems that may, in turn, cause economic losses. By spamming messages, we lose memory space, computing power, and speed. To remove these spam messages, we need to spend our time.

Robust tracking of a target in a clutter environment is an important and challenging task. In recent years, the nearest neighbor methods and probabilistic data association filters were proposed. However, the performance of these methods diminishes as the number of measurements increases. In this paper, we propose a robust generative approach to effectively model multiple sensor measurements for tracking a moving target in an environment with high clutter. We assume a time-dependent number of measurements that include sensor observations with unknown origin, some of which may only contain clutter with no additional information. We robustly and accurately estimate the trajectory of the moving target in a high clutter environment with an unknown number of clutters by employing Bayesian nonparametric modeling. In particular, we employ a class of joint Bayesian nonparametric models to construct the joint prior distribution of target and clutter measurements such that the conditional distributions follow a Dirichlet process. The marginalized Dirichlet process prior of the target measurements is then used in a Bayesian tracker to estimate the dynamically-varying target state. We show through experiments that the tracking performance and effectiveness of our proposed framework are increased by suppressing high clutter measurements. In addition, we show that our proposed method outperforms existing methods such as nearest neighbor and probability data association filters.

The paper proposes a new hybrid Bayesian network learning algorithm, termed Forward Early Dropping Hill Climbing (FEDHC), designed to work with either continuous or categorical data. FEDHC consists of a skeleton identification phase (learning the conditional associations among the variables) followed by the scoring phase that assigns the causal directions. Specifically for the case of continuous data, a robust to outliers version of FEDHC is also proposed. The paper manifests that the only implementation of MMHC in the statistical software \textit{R}, is prohibitively expensive and a new implementation is offered. The FEDHC is tested via Monte Carlo simulations that distinctly show it is computationally efficient, and produces Bayesian networks of similar to, or of higher accuracy than MMHC and PCHC. FEDHC yields more accurate Bayesian networks than PCHC with continuous data but less accurate with categorical data. Finally, an application of FEDHC, PCHC and MMHC algorithms to real data, from the field of economics, is demonstrated using the statistical software \textit{R}.

A statistical analysis of the observed perturbations in the density of stellar streams can in principle set stringent contraints on the mass function of dark matter subhaloes, which in turn can be used to constrain the mass of the dark matter particle. However, the likelihood of a stellar density with respect to the stream and subhaloes parameters involves solving an intractable inverse problem which rests on the integration of all possible forward realisations implicitly defined by the simulation model. In order to infer the subhalo abundance, previous analyses have relied on Approximate Bayesian Computation (ABC) together with domain-motivated but handcrafted summary statistics. Here, we introduce a likelihood-free Bayesian inference pipeline based on Amortised Approximate Likelihood Ratios (AALR), which automatically learns a mapping between the data and the simulator parameters and obviates the need to handcraft a possibly insufficient summary statistic. We apply the method to the simplified case where stellar streams are only perturbed by dark matter subhaloes, thus neglecting baryonic substructures, and describe several diagnostics that demonstrate the effectiveness of the new method and the statistical quality of the learned estimator.

Predicting future states or actions of a given system remains a fundamental, yet unsolved challenge of intelligence, especially in the scope of complex and non-deterministic scenarios, such as modeling behavior of humans. Existing approaches provide results under strong assumptions concerning unimodality of future states, or, at best, assuming specific probability distributions that often poorly fit to real-life conditions. In this work we introduce a robust and flexible probabilistic framework that allows to model future predictions with virtually no constrains regarding the modality or underlying probability distribution. To achieve this goal, we leverage a hypernetwork architecture and train a continuous normalizing flow model. The resulting method dubbed RegFlow achieves state-of-the-art results on several benchmark datasets, outperforming competing approaches by a significant margin.

These topics are getting very hot nowadays because these learning algorithms can be used in several fields from software engineering to investment banking. Learning algorithms can recognize patterns which can help detect cancer for example or we may construct algorithms that can have a very good guess about stock prices movement in the market. In each section we will talk about the theoretical background for all of these algorithms then we are going to implement these problems together. We will use Python with SkLearn, Keras and TensorFlow. Machine Learning Algorithms: machine learning approaches are becoming more and more important even in 2020.

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and provide probabilistic uncertainty estimates, but can be computationally expensive to run. Cross-validation (CV) is therefore not a common practice to evaluate the predictive performance of BHRMs. Our method circumvents the need to re-run computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. By conditioning on the variance-covariance parameters, we shift the CV problem from probability-based sampling to a simple and familiar optimization problem. In many cases, this produces estimates which are equivalent to full CV. We provide theoretical results and demonstrate its efficacy on publicly available data and in simulations.