Learning Graphical Models
Elements of machine learning
The official title of this free book available in PDF format is Machine Learning Cheat Sheet. See table of content screenshot below. The chapters 17 to 28 (the most interesting ones in my opinion) seem like a work in progress - I'm sure the authors intend to make them a bit bigger. For a more modern and applied book, get Dr Granville's book on data science.
On Partial Information and Contradictions in Probabilistic Abstract Argumentation
Hunter, Anthony (University College London) | Thimm, Matthias (Universität Koblenz-Landau)
We provide new insights into the area of combining abstract argumentation frameworks with probabilistic reasoning. In particular, we consider the scenario when assessments on the probabilities of a subset of the arguments is given and the probabilities of the remaining arguments have to be derived, taking both the topology of the argumentation framework and principles of probabilistic reasoning into account. We generalize this scenario by also considering inconsistent assessments, i.e., assessments that contradict the topology of the argumentation framework. Building on approaches to inconsistency measurement, we present a general framework to measure the amount of conflict of these assessments and provide a method for inconsistent-tolerant reasoning.
DECT: Distributed Evolving Context Tree for Understanding User Behavior Pattern Evolution
Shu, Xiaokui (Virginia Polytechnic Institute and State University) | Laptev, Nikolay (Yahoo Labs) | Yao, Danfeng (Daphne) (Virginia Polytechnic Institute and State University)
Internet user behavior models characterize user browsing dynamics or the transitions among web pages. The models help Internet companies improve their services by accurately targeting customers and providing them the information they want. For instance, specific web pages can be customized and prefetched for individuals based on sequences of web pages they have visited. Existing user behavior models abstracted as time-homogeneous Markov models cannot efficiently model user behavior variation through time. This demo presents DECT, a scalable time-variant variable-order Markov model. DECT digests terabytes of user session data and yields user behavior patterns through time. We realize DECT using Apache Spark and deploy it on top of Yahoo! infrastructure. We demonstrate the benefits of DECT with anomaly detection and ad click rate prediction applications. DECT enables the detection of higher-order path anomalies and provides deep insights into ad click rates with respect to user visiting paths.
Solving PP PP -Complete Problems Using Knowledge Compilation
Oztok, Umut (University of California, Los Angeles) | Choi, Arthur (University of California, Los Angeles) | Darwiche, Adnan (University of California, Los Angeles)
Knowledge compilation has been successfully used to solve beyond NP problems, including some PP-complete and NP PP -complete problems for Bayesian networks. In this work we show how knowledge compilation can be used to solve problems in the more intractable complexity class PP^PP. This class contains NP PP and includes interesting AI problems, such as non-myopic value of information. We show how to solve the prototypical PP PP -complete problem MajMajsat in linear-time once the problem instance is compiled into a special class of Sentential Decision Diagrams. To show the practical value of our approach, we adapt it to answer the Same-Decision Probability (SDP) query, which was recently introduced for Bayesian networks. The SDP problem is also PP PP P-complete. It is a value-of-information query that quantifies the robustness of threshold-based decisions and comes with a corresponding algorithm that was also recently proposed. We present favorable experimental results, comparing our new algorithm based on knowledge compilation with the state-of-the-art algorithm for computing the SDP.
Probabilistic Models over Weighted Orderings: Fixed-Parameter Tractable Variable Elimination
Lukasiewicz, Thomas (University of Oxford) | Martinez, Maria Vanina (Universidad Nacional del Sur) | Poole, David (University of British Columbia) | Simari, Gerardo Ignacio (Universidad Nacional del Sur)
Probabilistic models with weighted formulas, known as Markov models or log-linear models, are used in many domains. Recent models of weighted orderings between elements that have been proposed as flexible tools to express preferences under uncertainty, are also potentially useful in applications like planning, temporal reasoning, and user modeling. Their computational properties are very different from those of conventional Markov models; because of the transitivity of the “less than” relation, standard methods that exploit structure of the models, such as variable elimination, are not directly applicable, as there are no conditional independencies between the orderings within connected components. The best known algorithms for general inference inthese models are exponential in the number of statements. Here, we present the first algorithms that exploit the available structure. We begin with the special case of models in the form of chains; we present an exact O(n^3) algorithm, where n is the total number of elements. Next, we generalize this technique to models in which the set of statements are comprised of arbitrary sets of atomic weighted preference formulas (while the query and evidence are conjunctions of atomic preference formulas), and the resulting exact algorithm runs in time O(m * n^2 * n^c), where m is the number of preference formulas, n is the number of elements, and c is the maximum number of elements in a linear cut (which depends both on the structure of the model and the order in which the elements are processed)—therefore, this algorithm is tractable for cases in which c can be bounded to a low value. Finally, we report on the results of an empirical evaluation of both algorithms, showing how they scale with reasonably-sized models.
Weighted Rules under the Stable Model Semantics
Lee, Joohyung (Arizona State University) | Wang, Yi (Arizona State University)
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.
Bayesian Deduction with Subjective Opinions
Ivanovska, Magdalena (University of Oslo) | Jøsang, Audun (University of Oslo) | Sambo, Francesco ( University of Padova )
Subjective opinions can represent uncertain probabilistic information of any kind, minor or major A Bayesian network (BN) is a compact representation of a imprecision and even total ignorance about the probability joint probability distribution in the form of a directed acyclic distribution, by varying the uncertainty mass between 0 and graph (DAG) with random variables as nodes, and a set 1. By simply substituting every input conditional probability of conditional probability distributions associated with each distribution in a BN with a subjective opinion, we obtain node representing the probabilistic connection of the node what we call a subjective Bayesian network.
Bounded Optimal Exploration in MDP
Kawaguchi, Kenji (Massachusetts Institute of Technology)
Within the framework of probably approximately correct Markov decision processes (PAC-MDP), much theoretical work has focused on methods to attain near optimality after a relatively long period of learning and exploration. However, practical concerns require the attainment of satisfactory behavior within a short period of time. In this paper, we relax the PAC-MDP conditions to reconcile theoretically driven exploration methods and practical needs. We propose simple algorithms for discrete and continuous state spaces, and illustrate the benefits of our proposed relaxation via theoretical analyses and numerical examples. Our algorithms also maintain anytime error bounds and average loss bounds. Our approach accommodates both Bayesian and non-Bayesian methods.
Modeling Human Understanding of Complex Intentional Action with a Bayesian Nonparametric Subgoal Model
Nakahashi, Ryo (Sony Corporation) | Baker, Chris L. (Massachusetts Institute of Technology) | Tenenbaum, Joshua B. (Massachusetts Institute of Technology)
Most human behaviors consist of multiple parts, steps, or subtasks. These structures guide our ac- tion planning and execution, but when we observe others, the latent structure of their actions is typ- ically unobservable, and must be inferred in order to learn new skills by demonstration, or to as- sist others in completing their tasks. For example, an assistant who has learned the subgoal struc- ture of a colleague’s task can more rapidly rec- ognize and support their actions as they unfold. Here we model how humans infer subgoals from observations of complex action sequences using a nonparametric Bayesian model, which assumes that observed actions are generated by approxi- mately rational planning over unknown subgoal sequences. We test this model with a behavioral experiment in which humans observed different se- ries of goal-directed actions, and inferred both the number and composition of the subgoal sequences associated with each goal. The Bayesian model predicts human subgoal inferences with high ac- curacy, and significantly better than several al- ternative models and straightforward heuristics. Motivated by this result, we simulate how learn- ing and inference of subgoals can improve perfor- mance in an artificial user assistance task. The Bayesian model learns the correct subgoals from fewer observations, and better assists users by more rapidly and accurately inferring the goal of their actions than alternative approaches.
Discriminative Nonparametric Latent Feature Relational Models with Data Augmentation
Chen, Bei (Tsinghua University) | Chen, Ning (Tsinghua University) | Zhu, Jun ( Tsinghua University ) | Song, Jiaming ( Tsinghua University ) | Zhang, Bo ( Tsinghua University )
We present a discriminative nonparametric latent feature relational model (LFRM) for link prediction to automatically infer the dimensionality of latent features. Under the generic RegBayes (regularized Bayesian inference) framework, we handily incorporate the prediction loss with probabilistic inference of a Bayesian model; set distinct regularization parameters for different types of links to handle the imbalance issue in real networks; and unify the analysis of both the smooth logistic log-loss and the piecewise linear hinge loss. For the nonconjugate posterior inference, we present a simple Gibbs sampler via data augmentation, without making restricting assumptions as done in variational methods. We further develop an approximate sampler using stochastic gradient Langevin dynamics to handle large networks with hundreds of thousands of entities and millions of links, orders of magnitude larger than what existing LFRM models can process. Extensive studies on various real networks show promising performance.