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 Bayesian Learning


How to Calibrate the Scores of Biased Reviewers by Quadratic Programming

AAAI Conferences

Peer reviewing is the key ingredient of evaluating the quality of scientific work. Based on the review scores assigned by the individual reviewers to the submissions, program committees of conferences and journal editors decide which papers to accept for publication and which to reject. However, some reviewers may be more rigorous than others, they may be biased one way or the other, and they often have highly subjective preferences over the papers they review. Moreover, each reviewer usually has only a very local view, as he or she evaluates only a small fraction of the submissions. Despite all these shortcomings, the review scores obtained need to be aggregrated in order to globally rank all submissions and to make the acceptance/rejection decision. A common method is to simply take the average of each submission's review scores, possibly weighted by the reviewers' confidence levels. Unfortunately, the global ranking thus produced often suffers a certain unfairness, as the reviewers' biases and limitations are not taken into account. We propose a method for calibrating the scores of reviewers that are potentially biased and blindfolded by having only partial information. Our method uses a maximum likelihood estimator, which estimates both the bias of each individual reviewer and the unknown "ideal" score of each submission. This yields a quadratic program whose solution transforms the individual review scores into calibrated, globally comparable scores. We argue why our method results in a fairer and more reasonable global ranking than simply taking the average of scores. To show its usefulness, we test our method empirically using real-world data.


Spectrum-Based Sequential Diagnosis

AAAI Conferences

We present a spectrum-based, sequential software debugging approach coined Sequoia, that greedily selects tests out of a suite of tests to narrow down the set of diagnostic candidates with a minimum number of tests. Sequoia handles multiple faults, that can be intermittent, at polynomial time and space complexity, due to a novel, approximate diagnostic entropy estimation approach, which considers the subset of diagnoses that cover almost all Bayesian posterior probability mass. Synthetic experiments show that Sequoia achieves much better diagnostic uncertainty reduction compared to random test sequencing.Real programs, taken from the Software Infrastructure Repository, confirm Sequoia's better performance, with a test reduction up to 80% compared to random test sequences.


Limits of Preprocessing

AAAI Conferences

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a complexity theoretic assumption, none of the considered problems can be reduced by polynomial-time preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, such as induced width or backdoor size. Our results provide a firm theoretical boundary for the performance of polynomial-time preprocessing algorithms for the considered problems.


A Data Mining Approach to the Diagnosis of Tuberculosis by Cascading Clustering and Classification

arXiv.org Artificial Intelligence

In this paper, a methodology for the automated detection and classification of Tuberculosis(TB) is presented. Tuberculosis is a disease caused by mycobacterium which spreads through the air and attacks low immune bodies easily. Our methodology is based on clustering and classification that classifies TB into two categories, Pulmonary Tuberculosis(PTB) and retroviral PTB(RPTB) that is those with Human Immunodeficiency Virus (HIV) infection. Initially K-means clustering is used to group the TB data into two clusters and assigns classes to clusters. Subsequently multiple different classification algorithms are trained on the result set to build the final classifier model based on K-fold cross validation method. This methodology is evaluated using 700 raw TB data obtained from a city hospital. The best obtained accuracy was 98.7% from support vector machine (SVM) compared to other classifiers. The proposed approach helps doctors in their diagnosis decisions and also in their treatment planning procedures for different categories.


Adaptive Gaussian Predictive Process Approximation

arXiv.org Machine Learning

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation crucially depends on a set of points, called knots, at which the original process is retained, while the rest is approximated via a deterministic extrapolation. Knots should be few in number to keep the computational complexity low, but provide a good coverage of the process domain to limit approximation error. We present theoretical calculations to show that coverage must be judged by the canonical metric of the Gaussian process. This necessitates having in place a knots selection algorithm that automatically adapts to the changes in the canonical metric affected by changes in the parameter values controlling the Gaussian process covariance function. We present an algorithm toward this by employing an incomplete Cholesky factorization with pivoting and dynamic stopping. Although these concepts already exist in the literature, our contribution lies in unifying them into a fast algorithm and in using computable error bounds to finesse implementation of the predictive process approximation. The resulting adaptive predictive process offers a substantial automatization of Guassian process model fitting, especially for Bayesian applications where thousands of values of the covariance parameters are to be explored.


A Sequence of Relaxations Constraining Hidden Variable Models

arXiv.org Artificial Intelligence

Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that model. Our main contribution is to introduce a sequence of relaxations which provides progressively tighter hidden variable tests. We demonstrate applicability to mixtures of sequences of i.i.d. variables, Bell inequalities, and homophily models in social networks. For the last, we demonstrate that our method provides a test that is able to rule out latent homophily as the sole explanation for correlations on a real social network that are known to be due to influence.


New Complexity Results for MAP in Bayesian Networks

AAAI Conferences

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.


Short Text Conceptualization Using a Probabilistic Knowledgebase

AAAI Conferences

Most of the text mining tasks, such as clustering, is dominated by statistical approaches that treat text as a bag of words. Semantics in the text is largely ignored in the mining process, and the mining results are often not easily interpretable. One particular challenge faced by such approaches is short text understanding, as short text lacks enough content from which a statistical conclusion can be drawn. For example, traditional topic analysis methods consider topic segments with tens of hundreds of words. Latent topic modeling, such as latent Dirichlet allocation, also requires sufficient words to infer document topic distribution. We enhance machine learning algorithms by first giving the machine a probabilistic knowledgebase that contains as big, rich, and consistent concepts (of worldly facts) as those in our mental world. Then a Bayesian inference mechanism is developed to conceptualize words and short text. We conducted comprehensive tests of our method on conceptualizing set of text terms, as well as clustering Twitter messages (tweets), which are typically approximately ten words long. Compared to latent semantic topic modeling and other four kinds of methods that using WordNet, Freebase and Wikipedia (category links and explicit semantic analysis), we show significant improvements in terms of tweets clustering accuracy.


Bayesian Abductive Logic Programs: A Probabilistic Logic for Abductive Reasoning

AAAI Conferences

In this proposal, we introduce Bayesian Abductive Logic Programs (BALP), a probabilistic logic that adapts Bayesian Logic Programs (BLPs) for abductive reasoning. Like BLPs, BALPs also combine first-order logic and Bayes nets. However, unlike BLPs, which use deduction to construct Bayes nets, BALPs employ logical abduction. As a result, BALPs are more suited for problems like plan/activity recognition that require abductive reasoning. In order to demonstrate the efficacy of BALPs, we apply it to two abductive reasoning tasks — plan recognition and natural language understanding.