The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex

Modelling fixation locations using spatial point processes

Whenever eye movements are measured, a central part of the analysis has to do with where subjects fixate, and why they fixated where they fixated. To a first approximation, a set of fixations can be viewed as a set of points in space: this implies that fixations are spatial data and that the analysis of fixation locations can be beneficially thought of as a spatial statistics problem. We argue that thinking of fixation locations as arising from point processes is a very fruitful framework for eye movement data, helping turn qualitative questions into quantitative ones. We provide a tutorial introduction to some of the main ideas of the field of spatial statistics, focusing especially on spatial Poisson processes. We show how point processes help relate image properties to fixation locations. In particular we show how point processes naturally express the idea that image features' predictability for fixations may vary from one image to another. We review other methods of analysis used in the literature, show how they relate to point process theory, and argue that thinking in terms of point processes substantially extends the range of analyses that can be performed and clarify their interpretation.Comment: Revised following peer revie

Improving Pure-Tone Audiometry Using Probabilistic Machine Learning Classification

Hearing loss is a critical public health concern, affecting hundreds millions of people worldwide and dramatically impacting quality of life for affected individuals. While treatment techniques have evolved in recent years, methods for assessing hearing ability have remained relatively unchanged for decades. The standard clinical procedure is the modified Hughson-Westlake procedure, an adaptive pure-tone detection task that is typically performed manually by audiologists, costing millions of collective hours annually among healthcare professionals. In addition to the high burden of labor, the technique provides limited detail about an individual’s hearing ability, estimating only detection thresholds at a handful of pre-defined pure-tone frequencies (a threshold audiogram). An efficient technique that produces a detailed estimate of the audiometric function, including threshold and spread, could allow for better characterization of particular hearing pathologies and provide more diagnostic value. Parametric techniques exist to efficiently estimate multidimensional psychometric functions, but are ill-suited for estimation of audiometric functions because these functions cannot be easily parameterized. The Gaussian process is a compelling machine learning technique for inference of nonparametric multidimensional functions using binary data. The work described in this thesis utilizes Gaussian process classification to build an automated framework for efficient, high-resolution estimation of the full audiometric function, which we call the machine learning audiogram (MLAG). This Bayesian technique iteratively computes a posterior distribution describing its current belief about detection probability given the current set of observed pure tones and detection responses. The posterior distribution can be used to provide a current point estimate of the psychometric function as well as to select an informative query point for the next stimulus to be provided to the listener. The Gaussian process covariance function encodes correlations between variables, reflecting prior beliefs on the system; MLAG uses a composite linear/squared exponential covariance function that enforces monotonicity with respect to intensity but only smoothness with respect to frequency for the audiometric function. This framework was initially evaluated in human subjects for threshold audiogram estimation. 2 repetitions of MLAG and 1 repetition of manual clinical audiometry were conducted in each of 21 participants. Results indicated that MLAG both agreed with clinical estimates and exhibited test-retest reliability to within accepted clinical standards, but with significantly fewer tone deliveries required compared to clinical methods while also providing an effectively continuous threshold estimate along frequency. This framework’s ability to evaluate full psychometric functions was then evaluated using simulated experiments. As a feasibility check, performance for estimating unidimensional psychometric functions was assessed and directly compared to inference using standard maximum-likelihood probit regression; results indicated that the two methods exhibited near identical performance for estimating threshold and spread. MLAG was then used to estimate 2-dimensional audiometric functions constructed using existing audiogram phenotypes. Results showed that this framework could estimate both threshold and spread of the full audiometric function with high accuracy and reliability given a sufficient sample count; non-active sampling using the Halton set required between 50-100 queries to reach clinical reliability, while active sampling strategies reduced the required number to around 20-30, with Bayesian active leaning by disagreement exhibiting the best performance of the tested methods. Overall, MLAG’s accuracy, reliability, and high degree of detail make it a promising method for estimation of threshold audiograms and audiometric functions, and the framework’s flexibility enables it to be easily extended to other psychophysical domains

Active learning of neural response functions with Gaussian processes

A sizeable literature has focused on the problem of estimating a low-dimensional feature space for a neuron’s stimulus sensitivity. However, comparatively little work has addressed the problem of estimating the nonlinear function from feature space to spike rate. Here, we use a Gaussian process (GP) prior over the infinitedimensional space of nonlinear functions to obtain Bayesian estimates of the “nonlinearity” in the linear-nonlinear-Poisson (LNP) encoding model. This approach offers increased flexibility, robustness, and computational tractability compared to traditional methods (e.g., parametric forms, histograms, cubic splines). We then develop a framework for optimal experimental design under the GP-Poisson model using uncertainty sampling. This involves adaptively selecting stimuli according to an information-theoretic criterion, with the goal of characterizing the nonlinearity with as little experimental data as possible. Our framework relies on a method for rapidly updating hyperparameters under a Gaussian approximation to the posterior. We apply these methods to neural data from a color-tuned simple cell in macaque V1, characterizing its nonlinear response function in the 3D space of cone contrasts. We find that it combines cone inputs in a highly nonlinear manner. With simulated experiments, we show that optimal design substantially reduces the amount of data required to estimate these nonlinear combination rules.