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.

We consider the problem of estimating the underlying graph associated with a Markov random field, with the added twist that the decoding algorithm can iteratively choose which subsets of nodes to sample based on the previous samples, resulting in an active learning setting. Considering both Ising and Gaussian models, we provide algorithm-independent lower bounds for high-probability recovery within the class of degree-bounded graphs. Our main results are minimax lower bounds for the active setting that match the best known lower bounds for the passive setting, which in turn are known to be tight in several cases of interest. Our analysis is based on Fano's inequality, along with novel mutual information bounds for the active learning setting, and the application of restricted graph ensembles. While we consider ensembles that are similar or identical to those used in the passive setting, we require different analysis techniques, with a key challenge being bounding a mutual information quantity associated with observed subsets of nodes, as opposed to full observations.

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.

Prior work on viewing plan recognition as parsing of grammars has assumed completely observable actions. This paper provides an algorithm to rewrite plan grammars to allow for recognizing partially observable actions.  For the ELEXIR (Geib 2009) system, the impact of this rewriting on plan recognition runtime is shown to be limited to those plans that actually use the partially observable actions.

In this paper, we focus on the problem of learning a Bayesian network over distributed data stored in a commodity cluster. Specifically, we address the challenge of computing the scoring function over distributed data in a scalable manner, which is a fundamental task during learning. We propose a novel approach designed to achieve: (a) scalable score computation using the principle of gossiping; (b) lower resource consumption via a probabilistic approach for maintaining scores using the properties of a Markov chain; and (c) effective distribution of tasks during score computation (on large datasets) by synergistically combining well-known hashing techniques. Through theoretical analysis, we show that our approach is superior to a MapReduce-style computation in terms of communication bandwidth. Further, it is superior to the batch-style processing of MapReduce for recomputing scores when new data are available.

When machine learning algorithms are used in life-critical or mission-critical applications (e.g., self driving cars, cyber security, surgical robotics), it is important to ensure that they provide some high-level correctness guarantees. We introduce a paradigm called Trusted Machine Learning (TML) with the goal of making learning techniques more trustworthy. We outline methods that show how symbolic analysis (specifi- cally parametric model checking) can be used to learn the dynamical model of a system where the learned model satis- fies correctness requirements specified in the form of temporal logic properties (e.g., safety, liveness). When a learned model does not satisfy the desired guarantees, we try two approaches: (1) Model Repair, wherein we modify a learned model directly, and (2) Data Repair, wherein we modify the data so that re-learning from the modified data will result in a trusted model. Model Repair tries to make the minimal changes to the trained model while satisfying the properties, whereas Data Repair tries to make the minimal changes to the dataset used to train the model for ensuring satisfaction of the properties. We show how the Model Repair and Data Repair problems can be solved for the case of probabilistic models, specifically Discrete-Time Markov Chains (DTMC) or Markov Decision Processes (MDP), when the desired properties are expressed in Probabilistic Computation Tree Logic (PCTL). Specifically, we outline how the parameter learning problem in the probabilistic Markov models under temporal logic constraints can be equivalently expressed as a non-linear optimization with non-linear rational constraints, by performing symbolic transformations using a parametric model checker. We illustrate the approach on two case studies: a controller for automobile lane changing, and query router for a wireless sensor network.