The goal of machine learning is to program computers to use example data or past experience to solve a given problem. Many successful applications of machine learning exist already, including systems that analyze past sales data to predict customer behavior, optimize robot behavior so that a task can be completed using minimum resources, and extract knowledge from bioinformatics data. Introduction to Machine Learning is a comprehensive textbook on the subject, covering a broad array of topics not usually included in introductory machine learning texts. Subjects include supervised learning; Bayesian decision theory; parametric, semi-parametric, and nonparametric methods; multivariate analysis; hidden Markov models; reinforcement learning; kernel machines; graphical models; Bayesian estimation; and statistical testing. Machine learning is rapidly becoming a skill that computer science students must master before graduation.

We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/multiresolution method for PDEs with rough ($L^\infty$) coefficients with rigorous a-priori accuracy and performance estimates. The method is discovered through a decision/game theory formulation of the problems of (1) identifying restriction and interpolation operators (2) recovering a signal from incomplete measurements based on norm constraints on its image under a linear operator (3) gambling on the value of the solution of the PDE based on a hierarchy of nested measurements of its solution or source term. The resulting elementary gambles form a hierarchy of (deterministic) basis functions of $H^1_0(\Omega)$ (gamblets) that (1) are orthogonal across subscales/subbands with respect to the scalar product induced by the energy norm of the PDE (2) enable sparse compression of the solution space in $H^1_0(\Omega)$ (3) induce an orthogonal multiresolution operator decomposition. The operating diagram of the multigrid method is that of an inverted pyramid in which gamblets are computed locally (by virtue of their exponential decay), hierarchically (from fine to coarse scales) and the PDE is decomposed into a hierarchy of independent linear systems with uniformly bounded condition numbers. The resulting algorithm is parallelizable both in space (via localization) and in bandwith/subscale (subscales can be computed independently from each other). Although the method is deterministic it has a natural Bayesian interpretation under the measure of probability emerging (as a mixed strategy) from the information game formulation and multiresolution approximations form a martingale with respect to the filtration induced by the hierarchy of nested measurements.

Bayesian inference is a way to get sharper predictions from your data. It's particularly useful when you don't have as much data as you would like and want to juice every last bit of predictive strength from it. Although it is sometimes described with reverence, Bayesian inference isn't magic or mystical. And even though the math under the hood can get dense, the concepts behind it are completely accessible. In brief, Bayesian inference lets you draw stronger conclusions from your data by folding in what you already know about the answer. Bayesian inference is based on the ideas of Thomas Bayes, a nonconformist Presbyterian minister in London about 300 years ago. He wrote two books, one on theology, and one on probability. His work included his now famous Bayes Theorem in raw form, which has since been applied to the problem of inference, the technical term for educated guessing. The popularity of Bayes' ideas was aided immeasurably by another minister, Richard Price. He saw their significance, refined them and published them. It would be more accurate and historically just to call Bayes' Theorem the Bayes-Price Rule.

Point patterns are sets or multi-sets of unordered elements that can be found in numerous data sources. However, in data analysis tasks such as classification and novelty detection, appropriate statistical models for point pattern data have not received much attention. This paper proposes the modelling of point pattern data via random finite sets (RFS). In particular, we propose appropriate likelihood functions, and a maximum likelihood estimator for learning a tractable family of RFS models. In novelty detection, we propose novel ranking functions based on RFS models, which substantially improve performance.

The use of Bayesian methods in large-scale data settings is attractive because of the rich hierarchical models, uncertainty quantification, and prior specification they provide. Standard Bayesian inference algorithms are computationally expensive, however, making their direct application to large datasets difficult or infeasible. Recent work on scaling Bayesian inference has focused on modifying the underlying algorithms to, for example, use only a random data subsample at each iteration. We leverage the insight that data is often redundant to instead obtain a weighted subset of the data (called a coreset) that is much smaller than the original dataset. We can then use this small coreset in any number of existing posterior inference algorithms without modification. In this paper, we develop an efficient coreset construction algorithm for Bayesian logistic regression models. We provide theoretical guarantees on the size and approximation quality of the coreset -- both for fixed, known datasets, and in expectation for a wide class of data generative models. Crucially, the proposed approach also permits efficient construction of the coreset in both streaming and parallel settings, with minimal additional effort. We demonstrate the efficacy of our approach on a number of synthetic and real-world datasets, and find that, in practice, the size of the coreset is independent of the original dataset size. Furthermore, constructing the coreset takes a negligible amount of time compared to that required to run MCMC on it.

Includes profile, demo downloads, and job openings. Developer of software systems that solve resource optimization, planning, scheduling, and deployment problems for the air transportation, gaming, healthcare, hospitality, and security industries. Source for neural network based data modeling, prediction, forecasting and optimization solutions. Areas of focus includes: Banking and Finance, Manufacturing, Marketing, Medical. Uses artificial-intelligence technologies to prevent fraud in transaction environments such as finance, e-commerce, telecommunications, and insurance.

Weighted model counting (WMC) has recently emerged as an effective and general approach to probabilistic inference, offering a computational framework for encoding a variety of formalisms, such as factor graphs and Bayesian networks.The advent of large-scale probabilistic knowledge bases has generated further interest in relational probabilistic representations, obtained by according weights to first-order formulas, whose semantics is given in terms of the ground theory, and solved by WMC. A fundamental limitation is that the domain of quantification, by construction and design, is assumed to be finite, which is at odds with areas such as vision and language understanding, where the existence of objects must be inferred from raw data. Dropping the finite-domain assumption has been known to improve the expressiveness of a first-order language for open-universe purposes, but these languages, so far, have eluded WMC approaches. In this paper, we revisit relational probabilistic models over an infinite domain, and establish a number of results that permit effective algorithms. We demonstrate this language on a number of examples, including a parameterized version of Pearl's Burglary-Earthquake-Alarm Bayesian network.

It may (2010) to estimate the probability of each possible goal be that one agent needs to monitor the activities of another based on the difference between the cost of the best plan agent, attempt to assist the other agent, or simply avoid getting for the goal given the observed actions, Cost(G O), and the in the way while performing its own duties. For all of cost of the best plan for the goal without the observed actions, these cases the agent needs to be able to realize what the Cost(G O). The big difference here is that the observations other agent is doing. In the absence of full and timely communication only indirectly give us probabilities for actions in of plans and goals, goal and plan recognition becomes the plan graph. We therefore first construct a Bayesian Network essential. Many goal recognition techniques allow the (BN) to estimate these action probabilities, and then sequence of observations to be incomplete, but few consider use this probability information in the plan graph to compute the possibility of noisy observations. In practice, this is not expected cost for each goal, given the observations.

A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these research domains is to develop methods that can estimate the posterior with few likelihood evaluations. In this paper, we study active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework. We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.

There is a widely-accepted need to revise current forms of health-care provision, with particular interest in sensing systems in the home. Given a multiple-modality sensor platform with heterogeneous network connectivity, as is under development in the Sensor Platform for HEalthcare in Residential Environment (SPHERE) Interdisciplinary Research Collaboration (IRC), we face specific challenges relating to the fusion of the heterogeneous sensor modalities. We introduce Bayesian models for sensor fusion, which aims to address the challenges of fusion of heterogeneous sensor modalities. Using this approach we are able to identify the modalities that have most utility for each particular activity, and simultaneously identify which features within that activity are most relevant for a given activity. We further show how the two separate tasks of location prediction and activity recognition can be fused into a single model, which allows for simultaneous learning an prediction for both tasks. We analyse the performance of this model on data collected in the SPHERE house, and show its utility. We also compare against some benchmark models which do not have the full structure,and show how the proposed model compares favourably to these methods