Combinatory Categorial Grammar (CCG) is a lexicalized grammar formalism in which words are associated with categories that, in combination with a small universal set of rules, specify the syntactic configurations in which they may occur. Categories are selected from a large, recursively-defined set; this leads to high word-to-category ambiguity, which is one of the primary factors that make learning CCG parsers difficult, especially in the face of little data. Previous work has shown that learning sequence models for CCG tagging can be improved by using linguistically-motivated prior probability distributions over potential categories. We extend this approach to the task of learning a CCG parser from weak supervision. We present a Bayesian formulation for CCG parser induction that assumes only supervision in the form of an incomplete tag dictionary mapping some word types to sets of potential categories. Our approach outperforms a baseline model trained with uniform priors by exploiting universal, intrinsic properties of the CCG formalism to bias the model toward simpler, more cross-linguistically common categories.
Understanding how housing values evolve over time is important to policy makers, consumers and real estate professionals. Existing methods for constructing housing indices are computed at a coarse spatial granularity, such as metropolitan regions, which can mask or distort price dynamics apparent in local markets, such as neighborhoods and census tracts. A challenge in moving to estimates at, for example, the census tract level is the sparsity of spatiotemporally localized house sales observations. Our work aims at addressing this challenge by leveraging observations from multiple census tracts discovered to have correlated valuation dynamics. Our proposed Bayesian nonparametric approach builds on the framework of latent factor models to enable a flexible, data-driven method for inferring the clustering of correlated census tracts. We explore methods for scalability and parallelizability of computations, yielding a housing valuation index at the level of census tract rather than zip code, and on a monthly basis rather than quarterly. Our analysis is provided on a large Seattle metropolitan housing dataset.
The most recent financial upheavals have cast doubt on the adequacy of some of the conventional quantitative risk management strategies, such as VaR (Value at Risk), in many common situations. Consequently, there has been an increasing need for verisimilar financial stress testings, namely simulating and analyzing financial portfolios in extreme, albeit rare scenarios. Unlike conventional risk management which exploits statistical correlations among financial instruments, here we focus our analysis on the notion of probabilistic causation, which is embodied by Suppes-Bayes Causal Networks (SBCNs); SBCNs are probabilistic graphical models that have many attractive features in terms of more accurate causal analysis for generating financial stress scenarios. In this paper, we present a novel approach for conducting stress testing of financial portfolios based on SBCNs in combination with classical machine learning classification tools. The resulting method is shown to be capable of correctly discovering the causal relationships among financial factors that affect the portfolios and thus, simulating stress testing scenarios with a higher accuracy and lower computational complexity than conventional Monte Carlo Simulations.
We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.
Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal non-homogeneity into such models by making the transition probabilities dependent on time-varying exogenous input variables via a multinomial logistic parametrization. We extend such models to introduce additional non-homogeneity into the emission distribution using a generalized linear model (GLM), with data augmentation for sampling-based inference. However, the presence of the logistic function in the state transition model significantly complicates parameter inference for the overall model, particularly in a Bayesian context. To address this we extend the recently-proposed Polya-Gamma data augmentation approach to handle non-homogeneous hidden Markov models (NHMMs), allowing the development of an efficient Markov chain Monte Carlo (MCMC) sampling scheme. We apply our model and inference scheme to 30 years of daily rainfall in India, leading to a number of insights into rainfall-related phenomena in the region. Our proposed approach allows for fully Bayesian analysis of relatively complex NHMMs on a scale that was not possible with previous methods. Software implementing the methods described in the paper is available via the R package NHMM.