You know that you want to build a predictive model. You've framed your problem in terms of classification or regression. You've prepared some training data (which took an age). You've heard or experienced first hand that Random Forests, Elastic Net Regression or Deep Belief Networks are "the business" and so you're going to use one of these (you've probably already verified that these algorithms are appropriate to your problem based on their general capabilities: whether it be their ability to deal with real valued data, "big" streaming data, multiple classes and so on). However, no two algorithms are the same (if they were we'd simply have fewer to choose from). As such there are a host of questions that you may not have even thought to ask which could make or break your choice.

Joint state and parameter estimation is a core problem for dynamic Bayesian networks. Although modern probabilistic inference toolkits make it relatively easy to specify large and practically relevant probabilistic models, the silver bullet---an efficient and general online inference algorithm for such problems---remains elusive, forcing users to write special-purpose code for each application. We propose a novel blackbox algorithm -- a hybrid of particle filtering for state variables and assumed density filtering for parameter variables. It has following advantages: (a) it is efficient due to its online nature, and (b) it is applicable to both discrete and continuous parameter spaces . On a variety of toy and real models, our system is able to generate more accurate results within a fixed computation budget. This preliminary evidence indicates that the proposed approach is likely to be of practical use.

So you know the Bayes rule. How does it relate to machine learning? It can be quite difficult to grasp how the puzzle pieces fit together - we know it took us a while. This article is an introduction we wish we had back then. While we have some grasp on the matter, we're not experts, so the following might contain inaccuracies or even outright errors.

Machine learning is becoming a buzzword, everybody talks aboit it and few seem to be interested in the math underneath (I find statements like "I wanted to know more but all sources were too statistical/mathematical and I wanted more practical stuff"). Let me tell you something: You can't really use Machine Learning if you don't know the statistical/mathematical basis. I am really upset when I see a Youtube video of some guy in T-Shirt probably working at a large organization ranting about Machine Learning and Data Science, telling programmers that maths is easy to grasp. Everybody knows how to press a button or, if you force me, almost everybody knows how to fix something in their Windows control panel, but that does not mean we can trust them when talking about building a secure payment system, Everybody can use Mahout or the like but that does not mean he knows jack about what he is doing using Naive Bayes to predict the class from thre variables (x, y, z) where z x 2 and x belongs to the range [-1,1]. Machine Learning is just a fancy word for the statistical/mathematical tools lying underneath, whose objective is to extract something that we may loosely call knowledge (or something that we understand) from data (or something chaotic that we do not understand), so that computers may take action based on the inferred knowledge.

Here we discuss general applications of statistical models, whether they arise from data science, operations research, engineering, machine learning or statistics. We do not discuss specific algorithms such as decision trees, logistic regression, Bayesian modeling, Markov models, data reduction or feature selection. Instead, I discuss frameworks - each one using its own types of techniques and algorithms - to solve real life problems. Most of the entries below are found in Wikipedia, and I have used a few definitions or extracts from the relevant Wikipedia articles, in addition to personal contributions. Spatial dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear to be correlated, either positively or negatively. Methods for time series analyses may be divided into two classes: frequency-domain methods and time-domain methods.

We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of brain summary measures (volumetric and cortical thickness values) to single nucleotide polymorphism (SNPs) data and imposes penalization at two nested levels, the first corresponding to genes and the second corresponding to SNPs. Associated with each level in the penalty is a tuning parameter which corresponds to a hyperparameter in the hierarchical Bayesian formulation. Following previous work on Bayesian lassos we consider the estimation of tuning parameters through either hierarchical Bayes based on hyperpriors and Gibbs sampling or through empirical Bayes based on maximizing the marginal likelihood using a Monte Carlo EM algorithm. For the specific model under consideration we find that these approaches can lead to severe overshrinkage of the regression parameter estimates in the high-dimensional setting or when the genetic effects are weak. We demonstrate these problems through simulation examples and study an approximation to the marginal likelihood which sheds light on the cause of this problem. We then suggest an alternative approach based on the widely applicable information criterion (WAIC), an asymptotic approximation to leave-one-out cross-validation that can be computed conveniently within an MCMC framework.

This thesis focuses on gaining linguistic insights into textual discussions on a word level. It was of special interest to distinguish messages that constructively contribute to a discussion from those that are detrimental to them. Thereby, we wanted to determine whether "I"- and "You"-messages are indicators for either of the two discussion styles. These messages are nowadays often used in guidelines for successful communication. Although their effects have been successfully evaluated multiple times, a large-scale analysis has never been conducted. Thus, we used Wikipedia Articles for Deletion (short: AfD) discussions together with the records of blocked users and developed a fully automated creation of an annotated data set. In this data set, messages were labelled either constructive or disruptive. We applied binary classifiers to the data to determine characteristic words for both discussion styles. Thereby, we also investigated whether function words like pronouns and conjunctions play an important role in distinguishing the two. We found that "You"-messages were a strong indicator for disruptive messages which matches their attributed effects on communication. However, we found "I"-messages to be indicative for disruptive messages as well which is contrary to their attributed effects. The importance of function words could neither be confirmed nor refuted. Other characteristic words for either communication style were not found. Yet, the results suggest that a different model might represent disruptive and constructive messages in textual discussions better.

The present work proposes hybridization of Expectation-Maximization (EM) and K-Means techniques as an attempt to speed-up the clustering process. Though both K-Means and EM techniques look into different areas, K-means can be viewed as an approximate way to obtain maximum likelihood estimates for the means. Along with the proposed algorithm for hybridization, the present work also experiments with the Standard EM algorithm. Six different datasets are used for the experiments of which three are synthetic datasets. Clustering fitness and Sum of Squared Errors (SSE) are computed for measuring the clustering performance. In all the experiments it is observed that the proposed algorithm for hybridization of EM and K-Means techniques is consistently taking less execution time with acceptable Clustering Fitness value and less SSE than the standard EM algorithm. It is also observed that the proposed algorithm is producing better clustering results than the Cluster package of Purdue University.

Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. This paper extends linear system identification to a wide class of nonsmooth stable spline estimators, where regularization functionals and data misfits can be selected from a rich set of piecewise linear quadratic penalties. This class encompasses the 1-norm, huber, and vapnik, in addition to the least-squares penalty, and the approach allows linear inequality constraints on the unknown impulse response. We develop a customized interior point solver for the entire class of proposed formulations. By representing penalties through their conjugates, we allow a simple interface that enables the user to specify any piecewise linear quadratic penalty for misfit and regularizer, together with inequality constraints on the response. The solver is locally quadratically convergent, with O(n2(m+n)) arithmetic operations per iteration, for n impulse response coefficients and m output measurements. In the system identification context, where n << m, IPsolve is competitive with available alternatives, illustrated by a comparison with TFOCS and libSVM. The modeling framework is illustrated with a range of numerical experiments, featuring robust formulations for contaminated data, relaxation systems, and nonnegativity and unimodality constraints on the impulse response. Incorporating constraints yields significant improvements in system identification. The solver used to obtain the results is distributed via an open source code repository.

In previous discussions of Bayesian Inference we introduced Bayesian Statistics and considered how to infer a binomial proportion using the concept of conjugate priors. We discussed the fact that not all models can make use of conjugate priors and thus calculation of the posterior distribution would need to be approximated numerically. In this article we introduce the main family of algorithms, known collectively as Markov Chain Monte Carlo (MCMC), that allow us to approximate the posterior distribution as calculated by Bayes' Theorem. In particular, we consider the Metropolis Algorithm, which is easily stated and relatively straightforward to understand. It serves as a useful starting point when learning about MCMC before delving into more sophisticated algorithms such as Metropolis-Hastings, Gibbs Samplers and Hamiltonian Monte Carlo. Once we have described how MCMC works, we will carry it out using the open-source PyMC3 library, which takes care of many of the underlying implementation details, allowing us to concentrate on Bayesian modelling.