gaussian process


Interpreting AI Is More Than Black And White

#artificialintelligence

Any sufficiently advanced technology is indistinguishable from magic. In the world of artificial intelligence & machine learning (AI & ML), black- and white-box categorization of models and algorithms refers to their interpretability. That is, given a model trained to map data inputs to outputs (e.g. And just as the software testing dichotomy is high-level behavior vs low-level logic, only white-box AI methods can be readily interpreted to see the logic behind models' predictions. In recent years with machine learning taking over new industries and applications, where the number of users far outnumber experts that grok the models and algorithms, the conversation around interpretability has become an important one.


Gaussian process based nonlinear latent structure discovery in multivariate spike train data

Neural Information Processing Systems

A large body of recent work focuses on methods for extracting low-dimensional latent structure from multi-neuron spike train data. Most such methods employ either linear latent dynamics or linear mappings from latent space to log spike rates. Here we propose a doubly nonlinear latent variable model that can identify low-dimensional structure underlying apparently high-dimensional spike train data. We introduce the Poisson Gaussian-Process Latent Variable Model (P-GPLVM), which consists of Poisson spiking observations and two underlying Gaussian processes--one governing a temporal latent variable and another governing a set of nonlinear tuning curves. The use of nonlinear tuning curves enables discovery of low-dimensional latent structure even when spike responses exhibit high linear dimensionality (e.g., as found in hippocampal place cell codes).


Learning Gaussian Processes by Minimizing PAC-Bayesian Generalization Bounds

Neural Information Processing Systems

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To this end, we propose a method to learn GPs and their sparse approximations by directly optimizing a PAC-Bayesian bound on their generalization performance, instead of maximizing the marginal likelihood. Besides its theoretical appeal, we find in our evaluation that our learning method is robust and yields significantly better generalization guarantees than other common GP approaches on several regression benchmark datasets. Papers published at the Neural Information Processing Systems Conference.


Using Deep Belief Nets to Learn Covariance Kernels for Gaussian Processes

Neural Information Processing Systems

We show how to use unlabeled data and a deep belief net (DBN) to learn a good covariance kernel for a Gaussian process. We first learn a deep generative model of the unlabeled data using the fast, greedy algorithm introduced by Hinton et.al. If the data is high-dimensional and highly-structured, a Gaussian kernel applied to the top layer of features in the DBN works much better than a similar kernel applied to the raw input. Performance at both regression and classification can then be further improved by using backpropagation through the DBN to discriminatively fine-tune the covariance kernel. Papers published at the Neural Information Processing Systems Conference.


Robust Regression with Twinned Gaussian Processes

Neural Information Processing Systems

We propose a Gaussian process (GP) framework for robust inference in which a GP prior on the mixing weights of a two-component noise model augments the standard process over latent function values. This approach is a generalization of the mixture likelihood used in traditional robust GP regression, and a specialization of the GP mixture models suggested by Tresp (2000) and Rasmussen and Ghahramani (2002). The value of this restriction is in its tractable expectation propagation updates, which allow for faster inference and model selection, and better convergence than the standard mixture. An additional benefit over the latter method lies in our ability to incorporate knowledge of the noise domain to influence predictions, and to recover with the predictive distribution information about the outlier distribution via the gating process. The model has asymptotic complexity equal to that of conventional robust methods, but yields more confident predictions on benchmark problems than classical heavy-tailed models and exhibits improved stability for data with clustered corruptions, for which they fail altogether.


Bayesian estimation of orientation preference maps

Neural Information Processing Systems

Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements.


Modeling human function learning with Gaussian processes

Neural Information Processing Systems

Accounts of how people learn functional relationships between continuous variables have tended to focus on two possibilities: that people are estimating explicit functions, or that they are simply performing associative learning supported by similarity. We provide a rational analysis of function learning, drawing on work on regression in machine learning and statistics. Using the equivalence of Bayesian linear regression and Gaussian processes, we show that learning explicit rules and using similarity can be seen as two views of one solution to this problem. We use this insight to define a Gaussian process model of human function learning that combines the strengths of both approaches. Papers published at the Neural Information Processing Systems Conference.


Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes

Neural Information Processing Systems

Identification and comparison of nonlinear dynamical systems using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our method involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible without solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods. Papers published at the Neural Information Processing Systems Conference.


Analytical Results for the Error in Filtering of Gaussian Processes

Neural Information Processing Systems

Bayesian filtering of stochastic stimuli has received a great deal of attention re- cently. It has been applied to describe the way in which biological systems dy- namically represent and make decisions about the environment. There have been no exact results for the error in the biologically plausible setting of inference on point process, however. We present an exact analysis of the evolution of the mean- squared error in a state estimation task using Gaussian-tuned point processes as sensors. This allows us to study the dynamics of the error of an optimal Bayesian decoder, providing insights into the limits obtainable in this task.


Active learning of neural response functions with Gaussian processes

Neural Information Processing Systems

A sizable literature has focused on the problem of estimating a low-dimensional feature space capturing a neuron's stimulus sensitivity. However, comparatively little work has addressed the problem of estimating the nonlinear function from feature space to a neuron's output spike rate. Here, we use a Gaussian process (GP) prior over the infinite-dimensional space of nonlinear functions to obtain Bayesian estimates of the "nonlinearity" in the linear-nonlinear-Poisson (LNP) encoding model. This offers flexibility, robustness, and computational tractability compared to traditional methods (e.g., parametric forms, histograms, cubic splines). Most importantly, we develop a framework for optimal experimental design based on uncertainty sampling.