We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use the much criticized Dempster rule of combination, but only the very natural Dempster-Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our setup can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.

Formal grammars are a popular class of knowledge representation that is traditionally confined to the modeling of natural and computer languages. However, several extensions of grammars have been proposed over time to model other types of data such as images [1, 2, 3] and events [4, 5, 6]. One prominent type of extension is stochastic And-Or grammars (AOG) [2]. A stochastic AOG simultaneously models compositions (i.e., a large pattern is the composition of several small patterns arranged according to a certain configuration) and reconfigurations (i.e., a pattern may have several alternative configurations), and in this way it can compactly represent a probabilistic distribution over a large number of patterns. Stochastic AOGs can be used to parse data samples into their compositional structures, which help solve multiple tasks (such as classification, annotation, and segmentation of the data samples) in a unified manner. This work was supported by the National Natural Science Foundation of China (61503248).

Originally the term "machine learning" was defined as "... artificial generation of knowledge from experience," and the first studies have been performed with games, i.e., with the game of checkers [1]. Today, machine learning (ML) is the fastest growing technical field, at the intersection of informatics and statistics, tightly connected with data science and knowledge discovery, and health is among the greatest challenges [2, 3]. Particularly, probabilistic ML is extremely useful for health informatics, where most problems involve dealing with uncertainty. The theoretical basis for the probabilistic ML was laid by Thomas Bayes (1701–1761), [4, 5]. Probabilistic inference vastly influenced artificial intelligence and statistical learning and the inverse probability allows to infer unknowns, learn from data and make predictions [6, 7].

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. Feel free to point them out, either in the comments or privately.

Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated expression of modules (and module groups) of functionally related genes across the genome. Coregulation can also arise through the physical association of multi-gene complexes through chromosomal looping, which are then transcribed together. We present a general formalism for modeling coregulation rules in the framework of Random Boolean Networks (RBN), and develop specific models for transcription factor networks with modular structure (including module groups, and multi-input modules (MIM) with autoregulation) and multi-gene complexes (including hierarchical differentiation between multi-gene complex members). We develop a mean-field approach to analyse the stability of large networks incorporating coregulation, and show that autoregulated MIM and hierarchical gene-complex models can achieve greater stability than networks without coregulation whose rules have matching activation frequency. We provide further analysis of the stability of small networks of both kinds through simulations. We also characterize several general properties of the transients and attractors in the hierarchical coregulation model, and show using simulations that the steady-state distribution factorizes hierarchically as a Bayesian network in a Markov Jump Process analogue of the RBN model.

Its a constant that you use to normalize, right? And what comes after the normalizing constant in the equation is a vector, right? The authors are using Z' so that you know that the vector always gets normalized, you don't just calculate a constant at the start of training and reuse the same constant each time you calculate as the vector moves off normal.

While there may be millions of developers, there simply aren't enough data scientists to go around, and most of them are committed to working for large companies with big budgets and humongous data sets. Companies like Montreal-based Fuzzy.io are filling in the talent gap by offering an API to a set of artificial intelligence (AI) services that allows web and mobile developers to easily incorporate AI-based decision-making into their projects -- ranging from recommendations, to dynamic pricing decisions, and matching users in marketplaces. "Most of the existing ML development services are built to be used by data scientists or developers who have expertise in building AI/ML systems," said Fuzzy.io co-founder Matt Fogel. "Additionally, most of these tools require the developer to bring a great deal of data in order to train custom models. The company was founded by Fogel, who was the former produce vice president at Agendize, along with serial entrepreneur and developer Evan Prodromou. The company also recently added Kevin Fox, who, when he was at Google, helped create the user interfaces for Gmail and Google Calendar. These virtual intelligent machines use an adaptive rule base to translate pre-set, intuitive and vague "business rules" into a framework that can generate precise results. It could be as vague as "new", "old", "warm" and "good," as the company explains on its blog: "A fuzzy agent accepts some input variables and maps them onto fuzzy sets -- intuitive terms from the problem domain.

Covariance Is 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Structure discovery in graphical models is the determination of the topology of a graph that encodes conditional independence properties of the joint distribution of all variables in the model. For some class of probability distributions, an edge between two variables is present if and only if the corresponding entry in the precision matrix is non-zero. For a finite sample estimate of the precision matrix, entries close to zero may be due to low sample effects, or due to an actual association between variables; these two cases are not readily distinguishable. %Fisher provided a hypothesis test based on a parametric approximation to the distribution of an entry in the precision matrix of a Gaussian distribution, but this may not provide valid upper bounds on $p$-values for non-Gaussian distributions. Many related works on this topic consider potentially restrictive distributional or sparsity assumptions that may not apply to a data sample of interest, and direct estimation of the uncertainty of an estimate of the precision matrix for general distributions remains challenging. Consequently, we make use of results for $U$-statistics and apply them to the covariance matrix. By probabilistically bounding the distortion of the covariance matrix, we can apply Weyl's theorem to bound the distortion of the precision matrix, yielding a conservative, but sound test threshold for a much wider class of distributions than considered in previous works. The resulting test enables one to answer with statistical significance whether an edge is present in the graph, and convergence results are known for a wide range of distributions. The computational complexities is linear in the sample size enabling the application of the test to large data samples for which computation time becomes a limiting factor. We experimentally validate the correctness and scalability of the test on multivariate distributions for which the distributional assumptions of competing tests result in underestimates of the false positive ratio. By contrast, the proposed test remains sound, promising to be a useful tool for hypothesis testing for diverse real-world problems.

Feature extraction has gained increasing attention in the field of machine learning, as in order to detect patterns, extract information, or predict future observations from big data, the urge of informative features is crucial. The process of extracting features is highly linked to dimensionality reduction as it implies the transformation of the data from a sparse high-dimensional space, to higher level meaningful abstractions. This dissertation employs Neural Networks for distributed paragraph representations, and Latent Dirichlet Allocation to capture higher level features of paragraph vectors. Although Neural Networks for distributed paragraph representations are considered the state of the art for extracting paragraph vectors, we show that a quick topic analysis model such as Latent Dirichlet Allocation can provide meaningful features too. We evaluate the two methods on the CMU Movie Summary Corpus, a collection of 25,203 movie plot summaries extracted from Wikipedia. Finally, for both approaches, we use K-Nearest Neighbors to discover similar movies, and plot the projected representations using T-Distributed Stochastic Neighbor Embedding to depict the context similarities. These similarities, expressed as movie distances, can be used for movies recommendation. The recommended movies of this approach are compared with the recommended movies from IMDB, which use a collaborative filtering recommendation approach, to show that our two models could constitute either an alternative or a supplementary recommendation approach.