arXiv subjects

Matthew T. Harrison

Publications and source records attributed to Matthew T. Harrison.

15 recordsLinked to original sources

arXiv2025

Time-Averaged Drift Approximations are Inconsistent for Inference in Drift Diffusion Models

Drift diffusion models (DDMs) have found widespread use in computational neuroscience, cognitive science, mathematical psychology as well as other fields. They model evidence accumulation in simple decision tasks as a stochastic process drifting towards decision barriers. In models where the drift is both time-varying within a trial and variable across trials, the high computational cost for accurate likelihood evaluation has often led to the use of a computationally convenient surrogate for parameter inference, the time-averaged drift approximation (TADA). In each trial, TADA assumes that the time-varying drift rate can be replaced by its temporal average throughout the trial. This approach enables fast parameter inference using analytical likelihood formulas for DDMs with constant drift. In this work, we show that such an estimator is inconsistent: it does not converge to the true drift, posing a risk of biasing scientific conclusions when parameter estimates are obtained by TADA and similar approximations. We provide an elementary proof of this inconsistency in what is perhaps the simplest possible setting: a Brownian motion with piecewise constant drift hitting a one-sided upper boundary. Furthermore, numerical examples based on an attentional DDM (aDDM) show that using TADA leads to systematic misestimation of attentional effects in decision making and can lead to false conclusions in scientific hypothesis testing.

stat.ME↗

arXiv2025

Efficient Inference in First Passage Time Models

First passage time models describe the time it takes for a random process to exit a region of interest and are widely used across various scientific fields. Fast and accurate numerical methods for computing the likelihood function in these models are essential for efficient statistical inference of model parameters. Specifically, in computational cognitive neuroscience, generalized drift diffusion models (GDDMs) are an important class of first passage time models that describe the latent psychological processes underlying simple decision-making scenarios. GDDMs model the joint distribution over choices and response times as the first hitting time of a one-dimensional stochastic differential equation (SDE) to possibly time-varying upper and lower boundaries. They are widely applied to extract parameters associated with distinct cognitive and neural mechanisms. However, current likelihood computation methods struggle in common application scenarios in which drift rates dynamically vary within trials as a function of exogenous covariates (e.g., brain activity in specific regions or visual fixations). In this work, we propose a fast and flexible algorithm for computing the likelihood function of GDDMs based on a large class of SDEs satisfying the Cherkasov condition. Our method divides each trial into discrete stages, employs fast analytical results to compute stage-wise densities, and integrates these to compute the overall trial-wise likelihood. Numerical examples demonstrate that our method not only yields accurate likelihood evaluations for efficient statistical inference, but also considerably outperforms existing approaches in terms of speed.

stat.ME↗

arXiv2023

Optimizing Crop Management with Reinforcement Learning and Imitation Learning

Crop management, including nitrogen (N) fertilization and irrigation management, has a significant impact on the crop yield, economic profit, and the environment. Although management guidelines exist, it is challenging to find the optimal management practices given a specific planting environment and a crop. Previous work used reinforcement learning (RL) and crop simulators to solve the problem, but the trained policies either have limited performance or are not deployable in the real world. In this paper, we present an intelligent crop management system which optimizes the N fertilization and irrigation simultaneously via RL, imitation learning (IL), and crop simulations using the Decision Support System for Agrotechnology Transfer (DSSAT). We first use deep RL, in particular, deep Q-network, to train management policies that require all state information from the simulator as observations (denoted as full observation). We then invoke IL to train management policies that only need a limited amount of state information that can be readily obtained in the real world (denoted as partial observation) by mimicking the actions of the previously RL-trained policies under full observation. We conduct experiments on a case study using maize in Florida and compare trained policies with a maize management guideline in simulations. Our trained policies under both full and partial observations achieve better outcomes, resulting in a higher profit or a similar profit with a smaller environmental impact. Moreover, the partial-observation management policies are directly deployable in the real world as they use readily available information.

cs.AI↗

arXiv2017

Reduced Bias for respondent driven sampling: accounting for non-uniform edge sampling probabilities in people who inject drugs in Mauritius

People who inject drugs are an important population to study in order to reduce transmission of blood-borne illnesses including HIV and Hepatitis. In this paper we estimate the HIV and Hepatitis C prevalence among people who inject drugs, as well as the proportion of people who inject drugs who are female in Mauritius. Respondent driven sampling (RDS), a widely adopted link-tracing sampling design used to collect samples from hard-to-reach human populations, was used to collect this sample. The random walk approximation underlying many common RDS estimators assumes that each social relation (edge) in the underlying social network has an equal probability of being traced in the collection of the sample. This assumption does not hold in practice. We show that certain RDS estimators are sensitive to the violation of this assumption. In order to address this limitation in current methodology, and the impact it may have on prevalence estimates, we present a new method for improving RDS prevalence estimators using estimated edge inclusion probabilities, and apply this to data from Mauritius.

stat.AP↗

arXiv2016

The discriminative Kalman filter for nonlinear and non-Gaussian sequential Bayesian filtering

The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter have been proposed that incorporate linear approximations to nonlinear models, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, we argue that in cases where the dimensionality of observed variables greatly exceeds the dimensionality of state variables, a model for $p(\text{state}|\text{observation})$ proves both easier to learn and more accurate for latent space estimation. We derive and validate what we call the discriminative Kalman filter (DKF): a closed-form discriminative version of Bayesian filtering that readily incorporates off-the-shelf discriminative learning techniques. Further, we demonstrate that given mild assumptions, highly non-linear models for $p(\text{state}|\text{observation})$ can be specified. We motivate and validate on synthetic datasets and in neural decoding from non-human primates, showing substantial increases in decoding performance versus the standard Kalman filter.

stat.ML↗

arXiv2015

Mixture models with a prior on the number of components

A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures (MFM). While inference in MFMs can be done with methods such as reversible jump Markov chain Monte Carlo, it is much more common to use Dirichlet process mixture (DPM) models because of the relative ease and generality with which DPM samplers can be applied. In this paper, we show that, in fact, many of the attractive mathematical properties of DPMs are also exhibited by MFMs---a simple exchangeable partition distribution, restaurant process, random measure representation, and in certain cases, a stick-breaking representation. Consequently, the powerful methods developed for inference in DPMs can be directly applied to MFMs as well. We illustrate with simulated and real data, including high-dimensional gene expression data.

stat.ME↗

arXiv2013

Inconsistency of Pitman-Yor process mixtures for the number of components

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).

math.ST↗

arXiv2013

Exact sampling and counting for fixed-margin matrices

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence matrices and contingency tables.

stat.CO↗

arXiv2013

A Dynamic Programming Approach for Approximate Uniform Generation of Binary Matrices with Specified Margins

Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there are practical algorithms for approximate uniform sampling. Here it is shown how dynamic programming and recent asymptotic enumeration results can be used to simplify and improve a certain class of approximate uniform samplers. The dynamic programming perspective suggests interesting generalizations.

stat.CO↗

arXiv2013

Importance sampling for weighted binary random matrices with specified margins

A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums. This conditional distribution arises in a variety of applications and includes as a special case the uniform distribution over zero-one tables with specified margins. The algorithm uses dynamic programming to combine hard margin constraints, combinatorial approximations, and additional non-uniform weighting in a principled way to give state-of-the-art results.

stat.CO↗

arXiv2013

A simple example of Dirichlet process mixture inconsistency for the number of components

For data assumed to come from a finite mixture with an unknown number of components, it has become common to use Dirichlet process mixtures (DPMs) not only for density estimation, but also for inferences about the number of components. The typical approach is to use the posterior distribution on the number of components occurring so far --- that is, the posterior on the number of clusters in the observed data. However, it turns out that this posterior is not consistent --- it does not converge to the true number of components. In this note, we give an elementary demonstration of this inconsistency in what is perhaps the simplest possible setting: a DPM with normal components of unit variance, applied to data from a "mixture" with one standard normal component. Further, we find that this example exhibits severe inconsistency: instead of going to 1, the posterior probability that there is one cluster goes to 0.

math.ST↗

arXiv2011

Conditional Modeling and the Jitter Method of Spike Re-sampling: Supplement

This technical report accompanies the manuscript "Conditional Modeling and the Jitter Method of Spike Re-sampling." It contains further details, comments, references, and equations concerning various simulations and data analyses presented in that manuscript, as well as a self-contained Mathematical Appendix that provides a formal treatment of jitter-based spike re-sampling methods.

stat.ME↗

arXiv2011

Conservative Hypothesis Tests and Confidence Intervals using Importance Sampling

Importance sampling is a common technique for Monte Carlo approximation, including Monte Carlo approximation of p-values. Here it is shown that a simple correction of the usual importance sampling p-values creates valid p-values, meaning that a hypothesis test created by rejecting the null when the p-value is <= alpha will also have a type I error rate <= alpha. This correction uses the importance weight of the original observation, which gives valuable diagnostic information under the null hypothesis. Using the corrected p-values can be crucial for multiple testing and also in problems where evaluating the accuracy of importance sampling approximations is difficult. Inverting the corrected p-values provides a useful way to create Monte Carlo confidence intervals that maintain the nominal significance level and use only a single Monte Carlo sample. Several applications are described, including accelerated multiple testing for a large neurophysiological dataset and exact conditional inference for a logistic regression model with nuisance parameters.

stat.CO↗

arXiv2011

Exact Enumeration and Sampling of Matrices with Specified Margins

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling.

stat.CO↗

arXiv2007

The Generalized Asymptotic Equipartition Property: Necessary and Sufficient Conditions

Suppose a string $X_1^n=(X_1,X_2,...,X_n)$ generated by a memoryless source $(X_n)_{n\geq 1}$ with distribution $P$ is to be compressed with distortion no greater than $D\geq 0$, using a memoryless random codebook with distribution $Q$. The compression performance is determined by the ``generalized asymptotic equipartition property'' (AEP), which states that the probability of finding a $D$-close match between $X_1^n$ and any given codeword $Y_1^n$, is approximately $2^{-n R(P,Q,D)}$, where the rate function $R(P,Q,D)$ can be expressed as an infimum of relative entropies. The main purpose here is to remove various restrictive assumptions on the validity of this result that have appeared in the recent literature. Necessary and sufficient conditions for the generalized AEP are provided in the general setting of abstract alphabets and unbounded distortion measures. All possible distortion levels $D\geq 0$ are considered; the source $(X_n)_{n\geq 1}$ can be stationary and ergodic; and the codebook distribution can have memory. Moreover, the behavior of the matching probability is precisely characterized, even when the generalized AEP is not valid. Natural characterizations of the rate function $R(P,Q,D)$ are established under equally general conditions.

cs.IT↗