Frank D. Wood

A New Approach to Probabilistic Programming Inference

We introduce and demonstrate a new approach to inference in expressive probabilistic programming languages based on particle Markov chain Monte Carlo. Our approach is simple to implement and easy to parallelize. It applies to Turing-complete probabilistic programming languages and supports accurate inference in models that make use of complex control ow, including stochastic recursion. It also includes primitives from Bayesian nonparametric statistics. Our experiments show that this approach can be more ecient than previously introduced single-site Metropolis-Hastings methods.

A nonparametric Bayesian alternative to spike sorting

The analysis of extra-cellular neural recordings typically begins with careful spike sorting and all analysis of the data then rests on the correctness of the resulting spike trains. In many situations this is unproblematic as experimental and spike sorting procedures often focus on well isolated units. There is evidence in the literature, however, that errors in spike sorting can occur even with carefully collected and selected data. Additionally, chronically implanted electrodes and arrays with fixed electrodes cannot be easily adjusted to provide well isolated units. In these situations, multiple units may be recorded and the assignment of waveforms to units may be ambiguous. At the same time, analysis of such data may be both scientifically important and clinically relevant. In this paper we address this issue using a novel probabilistic model that accounts for several important sources of uncertainty and error in spike sorting. In lieu of sorting neural data to produce a single best spike train, we estimate a probabilistic model of spike trains given the observed data. We show how such a distribution over spike sortings can support standard neuroscientific questions while providing a representation of uncertainty in the analysis. As a representative illustration of the approach, we analyzed primary motor cortical tuning with respect to hand movement in data recorded with a chronic multi-electrode array in non-human primates. We found that the probabilistic analysis generally agrees with human sorters but suggests the presence of tuned units not detected by humans.

A stochastic memoizer for sequence data

We propose an unbounded-depth, hierarchical, Bayesian nonparametric model for discrete sequence data. This model can be estimated from a single training sequence, yet shares statistical strength between subsequent symbol predictive distributions in such a way that predictive performance generalizes well. The model builds on a specific parameterization of an unbounded-depth hierarchical Pitman-Yor process. We introduce analytic marginalization steps (using coagulation operators) to reduce this model to one that can be represented in time and space linear in the length of the training sequence. We show how to perform inference in such a model without truncation approximation and introduce fragmentation operators necessary to do predictive inference. We demonstrate the sequence memoizer by using it as a language model, achieving state-of-the-art results.

The sequence memoizer

Probabilistic models of sequences play a central role in most machine translation, automated speech recognition, lossless compression, spell-checking, and gene identification applications to name but a few. Unfortunately, real-world sequence data often exhibit long range dependencies which can only be captured by computationally challenging, complex models. Sequence data arising from natural processes also often exhibits power-law properties, yet common sequence models do not capture such properties. The sequence memoizer is a new hierarchical Bayesian model for discrete sequence data that captures long range dependencies and power-law characteristics, while remaining computationally attractive. Its utility as a language model and general purpose lossless compressor is demonstrated.

Diagnosis code assignment: models and evaluation metrics

Background and objective The volume of healthcare data is growing rapidly with the adoption of health information technology. We focus on automated ICD9 code assignment from discharge summary content and methods for evaluating such assignments. Methods We study ICD9 diagnosis codes and discharge summaries from the publicly available Multiparameter Intelligent Monitoring in Intensive Care II (MIMIC II) repository. We experiment with two coding approaches: one that treats each ICD9 code independently of each other (flat classifier), and one that leverages the hierarchical nature of ICD9 codes into its modeling (hierarchy-based classifier). We propose novel evaluation metrics, which reflect the distances among gold-standard and predicted codes and their locations in the ICD9 tree. Experimental setup, code for modeling, and evaluation scripts are made available to the research community. Results The hierarchy-based classifier outperforms the flat classifier with F-measures of 39.5% and 27.6%, respectively, when trained on 20 533 documents and tested on 2282 documents. While recall is improved at the expense of precision, our novel evaluation metrics show a more refined assessment: for instance, the hierarchy-based classifier identifies the correct sub-tree of gold-standard codes more often than the flat classifier. Error analysis reveals that gold-standard codes are not perfect, and as such the recall and precision are likely underestimated. Conclusions Hierarchy-based classification yields better ICD9 coding than flat classification for MIMIC patients. Automated ICD9 coding is an example of a task for which data and tools can be shared and for which the research community can work together to build on shared models and advance the state of the art.

A Non-Parametric Bayesian Approach to Spike Sorting

In this work we present and apply infinite Gaussian mixture modeling, a non-parametric Bayesian method, to the problem of spike sorting. As this approach is Bayesian, it allows us to integrate prior knowledge about the problem in a principled way. Because it is non-parametric we are able to avoid model selection, a difficult problem that most current spike sorting methods do not address. We compare this approach to using penalized log likelihood to select the best from multiple finite mixture models trained by expectation maximization. We show favorable offline sorting results on real data and discuss ways to extend our model to online applications

Inference in Hidden Markov Models with Explicit State Duration Distributions

In this letter, we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting of both discrete state-indicator and discrete state-duration random variables. In contrast to the implicit geometric state duration distribution possessed by the standard HMM, EDHMMs allow the direct parameterization and estimation of per-state duration distributions. As most duration distributions are defined over the positive integers, truncation or other approximations are usually required to perform EDHMM inference.

Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints

We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and termination. This involves measure theory, stochastic labelled transition systems, and functor categories, but admits intuitive computational readings, one of which views sampled random variables as dynamically allocated read-only variables. We apply our semantics to validate nontrivial equations underlying the correctness of certain compiler optimisations and inference algorithms such as sequential Monte Carlo simulation. The language enables defining probability distributions on higher-order functions, and we study their properties.Categories and Subject Descriptors CR-number [D.3]: Programming languages

Lossless Compression Based on the Sequence Memoizer

In this work we describe a sequence compression method based on combining a Bayesian nonparametric sequence model with entropy encoding. The model, a hierarchy of Pitman-Yor processes of unbounded depth previously proposed by Wood et al. [16] in the context of language modelling, allows modelling of long-range dependencies by allowing conditioning contexts of unbounded length. We show that incremental approximate inference can be performed in this model, thereby allowing it to be used in a text compression setting. The resulting compressor reliably outperforms several PPM variants on many types of data, but is particularly effective in compressing data that exhibits power law properties.

Statistical Analysis of the Non-stationarity of Neural Population Codes

Neural prosthetic technology has moved from the laboratory to clinical settings with human trials. The motor cortical control of devices in such settings raises important questions about the design of computational interfaces that produce stable and reliable control over a wide range of operating conditions. In particular, non-stationarity of the neural code across different behavioral conditions or attentional states becomes a potential issue. Non-stationarity has been previously observed in animals where the encoding model representing the mathematical relationship between neural population activity and behavioral variables such as hand motion changes over time. If such an encoding model is formed and learned during a particular training period, decoding performance (neural control) with the model may not be consistent during successive periods even when the same task is repeated. It is critical in both laboratory experiments and in clinical settings to be able to evaluate whether the representation of movement encoded by a neural population has changed or not. Such information can be used as a cue to retrain the system or as feedback to an adaptive decoding algorithm. To that end, we develop a statistical methodology to evaluate changes in the neural code over time using a generative probabilistic decoding model. The changes are evaluated by comparing the likelihoods of firing rates given similar distributions of 2D hand kinematics collected while a primate periodically performs a manual cursor control task. A comparison is performed by measuring a distance between probabilistic encoding models trained at different times. The statistical significance of the distance measurements are justified with a systematic statistical hypothesis test. The experimental results demonstrate that the likelihood changes over different periods with the change being greater when more distant periods are compared