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Carson C. Chow

Publications and source records attributed to Carson C. Chow.

At least 19 recordsLinked to original sources
arXiv2023

Autoencoded sparse Bayesian in-IRT factorization, calibration, and amortized inference for the Work Disability Functional Assessment Battery

The Work Disability Functional Assessment Battery (WD-FAB) is a multidimensional item response theory (IRT) instrument designed for assessing work-related mental and physical function based on responses to an item bank. In prior iterations it was developed using traditional means -- linear factorization and null hypothesis statistical testing for item partitioning/selection, and finally, posthoc calibration of disjoint unidimensional IRT models. As a result, the WD-FAB, like many other IRT instruments, is a posthoc model. Its item partitioning, based on exploratory factor analysis, is blind to the final nonlinear IRT model and is not performed in a manner consistent with goodness of fit to the final model. In this manuscript, we develop a Bayesian hierarchical model for self-consistently performing the following simultaneous tasks: scale factorization, item selection, parameter identification, and response scoring. This method uses sparsity-based shrinkage to obviate the linear factorization and null hypothesis statistical tests that are usually required for developing multidimensional IRT models, so that item partitioning is consistent with the ultimate nonlinear factor model. We also analogize our multidimensional IRT model to probabilistic autoencoders, specifying an encoder function that amortizes the inference of ability parameters from item responses. The encoder function is equivalent to the "VBE" step in a stochastic variational Bayesian expectation maximization (VBEM) procedure that we use for approxiamte Bayesian inference on the entire model. We use the method on a sample of WD-FAB item responses and compare the resulting item discriminations to those obtained using the traditional posthoc method.

stat.ME↗
arXiv2023

Interpretable (not just posthoc-explainable) heterogeneous survivor bias-corrected treatment effects for assignment of postdischarge interventions to prevent readmissions

We used survival analysis to quantify the impact of postdischarge evaluation and management (E/M) services in preventing hospital readmission or death. Our approach avoids a specific pitfall of applying machine learning to this problem, which is an inflated estimate of the effect of interventions, due to survivors bias -- where the magnitude of inflation may be conditional on heterogeneous confounders in the population. This bias arises simply because in order to receive an intervention after discharge, a person must not have been readmitted in the intervening period. After deriving an expression for this phantom effect, we controlled for this and other biases within an inherently interpretable Bayesian survival framework. We identified case management services as being the most impactful for reducing readmissions overall.

stat.ME↗
arXiv2023

Interpretable (not just posthoc-explainable) medical claims modeling for discharge placement to prevent avoidable all-cause readmissions or death

We developed an inherently interpretable multilevel Bayesian framework for representing variation in regression coefficients that mimics the piecewise linearity of ReLU-activated deep neural networks. We used the framework to formulate a survival model for using medical claims to predict hospital readmission and death that focuses on discharge placement, adjusting for confounding in estimating causal local average treatment effects. We trained the model on a 5% sample of Medicare beneficiaries from 2008 and 2011, based on their 2009--2011 inpatient episodes, and then tested the model on 2012 episodes. The model scored an AUROC of approximately 0.76 on predicting all-cause readmissions -- defined using official Centers for Medicare and Medicaid Services (CMS) methodology -- or death within 30-days of discharge, being competitive against XGBoost and a Bayesian deep neural network, demonstrating that one need-not sacrifice interpretability for accuracy. Crucially, as a regression model, we provide what blackboxes cannot -- the exact gold-standard global interpretation of the model, identifying relative risk factors and quantifying the effect of discharge placement. We also show that the posthoc explainer SHAP fails to provide accurate explanations.

cs.CY↗
arXiv2020

Sparse encoding for more-interpretable feature-selecting representations in probabilistic matrix factorization

Dimensionality reduction methods for count data are critical to a wide range of applications in medical informatics and other fields where model interpretability is paramount. For such data, hierarchical Poisson matrix factorization (HPF) and other sparse probabilistic non-negative matrix factorization (NMF) methods are considered to be interpretable generative models. They consist of sparse transformations for decoding their learned representations into predictions. However, sparsity in representation decoding does not necessarily imply sparsity in the encoding of representations from the original data features. HPF is often incorrectly interpreted in the literature as if it possesses encoder sparsity. The distinction between decoder sparsity and encoder sparsity is subtle but important. Due to the lack of encoder sparsity, HPF does not possess the column-clustering property of classical NMF -- the factor loading matrix does not sufficiently define how each factor is formed from the original features. We address this deficiency by self-consistently enforcing encoder sparsity, using a generalized additive model (GAM), thereby allowing one to relate each representation coordinate to a subset of the original data features. In doing so, the method also gains the ability to perform feature selection. We demonstrate our method on simulated data and give an example of how encoder sparsity is of practical use in a concrete application of representing inpatient comorbidities in Medicare patients.

cs.LG↗
arXiv2019

Probabilistically-autoencoded horseshoe-disentangled multidomain item-response theory models

Item response theory (IRT) is a non-linear generative probabilistic paradigm for using exams to identify, quantify, and compare latent traits of individuals, relative to their peers, within a population of interest. In pre-existing multidimensional IRT methods, one requires a factorization of the test items. For this task, linear exploratory factor analysis is used, making IRT a posthoc model. We propose skipping the initial factor analysis by using a sparsity-promoting horseshoe prior to perform factorization directly within the IRT model so that all training occurs in a single self-consistent step. Being a hierarchical Bayesian model, we adapt the WAIC to the problem of dimensionality selection. IRT models are analogous to probabilistic autoencoders. By binding the generative IRT model to a Bayesian neural network (forming a probabilistic autoencoder), one obtains a scoring algorithm consistent with the interpretable Bayesian model. In some IRT applications the black-box nature of a neural network scoring machine is desirable. In this manuscript, we demonstrate within-IRT factorization and comment on scoring approaches.

cs.LG↗
arXiv2019

Before and beyond the Wilson-Cowan equations

The Wilson-Cowan equations represent a landmark in the history of computational neuroscience. Among the insights Wilson and Cowan offered for neuroscience, they crystallized an approach to modeling neural dynamics and brain function. Although their iconic equations are used in various guises today, the ideas that led to their formulation and the relationship to other approaches are not well known. Here, we give a little context to some of the biological and theoretical concepts that lead to the Wilson-Cowan equations and discuss how to extend beyond them.

q-bio.NC↗
arXiv2015

The Universality of Cancer

Cancer has been characterized as a constellation of hundreds of diseases differing in underlying mutations and depending on cellular environments. Carcinogenesis as a stochastic physical process has been studied for over sixty years, but there is no accepted standard model. We show that the hazard rates of all cancers are characterized by a simple dynamic stochastic process on a half-line, with a universal linear restoring force balancing a universal simple Brownian motion starting from a universal initial distribution. Only a critical radius defining the transition from normal to tumorigenic genomes distinguishes between different cancer types when time is measured in cell--cycle units. Reparametrizing to chronological time units introduces two additional parameters: the onset of cellular senescence with age and the time interval over which this cessation in replication takes place. This universality implies that there may exist a finite separation between normal cells and tumorigenic cells in all tissue types that may be a viable target for both early detection and preventive therapy.

q-bio.TO↗
arXiv2014

Second-generation PLINK: rising to the challenge of larger and richer datasets

PLINK 1 is a widely used open-source C/C++ toolset for genome-wide association studies (GWAS) and research in population genetics. However, the steady accumulation of data from imputation and whole-genome sequencing studies has exposed a strong need for even faster and more scalable implementations of key functions. In addition, GWAS and population-genetic data now frequently contain probabilistic calls, phase information, and/or multiallelic variants, none of which can be represented by PLINK 1's primary data format. To address these issues, we are developing a second-generation codebase for PLINK. The first major release from this codebase, PLINK 1.9, introduces extensive use of bit-level parallelism, O(sqrt(n))-time/constant-space Hardy-Weinberg equilibrium and Fisher's exact tests, and many other algorithmic improvements. In combination, these changes accelerate most operations by 1-4 orders of magnitude, and allow the program to handle datasets too large to fit in RAM. This will be followed by PLINK 2.0, which will introduce (a) a new data format capable of efficiently representing probabilities, phase, and multiallelic variants, and (b) extensions of many functions to account for the new types of information. The second-generation versions of PLINK will offer dramatic improvements in performance and compatibility. For the first time, users without access to high-end computing resources can perform several essential analyses of the feature-rich and very large genetic datasets coming into use.

q-bio.GN↗
arXiv2014

Application of compressed sensing to genome wide association studies and genomic selection

We show that the signal-processing paradigm known as compressed sensing (CS) is applicable to genome-wide association studies (GWAS) and genomic selection (GS). The aim of GWAS is to isolate trait-associated loci, whereas GS attempts to predict the phenotypic values of new individuals on the basis of training data. CS addresses a problem common to both endeavors, namely that the number of genotyped markers often greatly exceeds the sample size. We show using CS methods and theory that all loci of nonzero effect can be identified (selected) using an efficient algorithm, provided that they are sufficiently few in number (sparse) relative to sample size. For heritability h2 = 1, there is a sharp phase transition to complete selection as the sample size is increased. For heritability values less than one, complete selection can still occur although the transition is smoothed. The transition boundary is only weakly dependent on the total number of genotyped markers. The crossing of a transition boundary provides an objective means to determine when true effects are being recovered; we discuss practical methods for detecting the boundary. For h2 = 0.5, we find that a sample size that is thirty times the number of nonzero loci is sufficient for good recovery.

q-bio.GN↗
arXiv2013

Generalized activity equations for spiking neural network dynamics

Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time scales - the spike duration time is much shorter than the inter-spike time, which is much shorter than any learning time scale. In numerical analysis, this is a classic stiff problem. Spiking neurons are also much more difficult to study analytically. One possible approach to making spiking networks more tractable is to augment mean field activity models with some information about spiking correlations. For example, such a generalized activity model could carry information about spiking rates and correlations between spikes self-consistently. Here, we will show how this can be accomplished by constructing a complete formal probabilistic description of the network and then expanding around a small parameter such as the inverse of the number of neurons in the network. The mean field theory of the system gives a rate-like description. The first order terms in the perturbation expansion keep track of covariances.

q-bio.NC↗
arXiv2013

The causal meaning of Fisher's average effect

In order to formulate the Fundamental Theorem of Natural Selection, Fisher defined the average excess and average effect of a gene substitution. Finding these notions to be somewhat opaque, some authors have recommended reformulating Fisher's ideas in terms of covariance and regression, which are classical concepts of statistics. We argue that Fisher intended his two averages to express a distinction between correlation and causation. On this view the average effect is a specific weighted average of the actual phenotypic changes that result from physically changing the allelic states of homologous genes. We show that the statistical and causal conceptions of the average effect, perceived as inconsistent by Falconer, can be reconciled if certain relationships between the genotype frequencies and non-additive residuals are conserved. There are certain theory-internal considerations favoring Fisher's original formulation in terms of causality; for example, the frequency-weighted mean of the average effects equaling zero at each locus becomes a derivable consequence rather than an arbitrary constraint. More broadly, Fisher's distinction between correlation and causation is of critical importance to gene-trait mapping studies and the foundations of evolutionary biology.

q-bio.PE↗
arXiv2009

Systematic fluctuation expansion for neural network activity equations

Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate while leaving out higher order statistics like correlations between firing. A stochastic theory of neural networks which includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations, i.e. they depend only upon the mean and specific correlations of interest, without an {\it ad hoc} criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean fieldrate equations alone.

q-bio.NC↗
arXiv2008

Competition between transients in the rate of approach to a fixed point

Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the use of Poincare maps and phase resetting curves, have been developed for the study of periodic orbits. However, the analysis of transient dynamics associated with solutions on their way to an attracting fixed point has not received much rigorous attention. This paper introduces methods for the study of such transient dynamics. In particular, we focus on the analysis of whether one component of a solution to a system of differential equations can overtake the corresponding component of a reference solution, given that both solutions approach the same stable node. We call this phenomenon tolerance, which derives from a certain biological effect. Here, we establish certain general conditions, based on the initial conditions associated with the two solutions and the properties of the vector field, that guarantee that tolerance does or does not occur in two-dimensional systems. We illustrate these conditions in particular examples, and we derive and demonstrate additional techniques that can be used on a case by case basis to check for tolerance. Finally, we give a full rigorous analysis of tolerance in two-dimensional linear systems.

math.DS↗
arXiv2008

The dynamics of human body weight change

An imbalance between energy intake and energy expenditure will lead to a change in body weight (mass) and body composition (fat and lean masses). A quantitative understanding of the processes involved, which currently remains lacking, will be useful in determining the etiology and treatment of obesity and other conditions resulting from prolonged energy imbalance. Here, we show that the long-term dynamics of human weight change can be captured by a mathematical model of the macronutrient flux balances and all previous models are special cases of this model. We show that the generic dynamical behavior of body composition for a clamped diet can be divided into two classes. In the first class, the body composition and mass are determined uniquely. In the second class, the body composition can exist at an infinite number of possible states. Surprisingly, perturbations of dietary energy intake or energy expenditure can give identical responses in both model classes and existing data are insufficient to distinguish between these two possibilities. However, this distinction is important for the efficacy of clinical interventions that alter body composition and mass.

q-bio.TO↗
arXiv2007

Correlations, fluctuations and stability of a finite-size network of coupled oscillators

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model.

nlin.AO↗
arXiv2006

A Kinetic Theory of Coupled Oscillators

We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is analogous to the BBGKY hierarchy in the kinetic theory of plasmas and gases. To calculate the lowest order system size effect, we truncate this hierarchy at second order and solve the resulting closed equations for the two-oscillator correlation function around the incoherent state. We use this correlation function to compute the fluctuations of the order parameter, including the effect of transients, and compare this computation with numerical simulations.

nlin.CD↗
arXiv2004

Existence and Stability of Standing Pulses in Neural Networks: II Stability

We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear gain function. When two standing single-pulse solutions coexist, the small pulse is unstable, and the large pulse is stable. The large single-pulse is bistable with the ``all-off'' state. This bistable localized activity may have strong implications for the mechanism underlying working memory. We show that dimple pulses have similar stability properties to large pulses but double pulses are unstable.

q-bio.NC↗