A Statistical Description of Neural Ensemble Dynamics

The growing use of multi-channel neural recording techniques in behaving animals has produced rich datasets that hold immense potential for advancing our understanding of how the brain mediates behavior. One limitation of these techniques is they do not provide important information about the underlying anatomical connections among the recorded neurons within an ensemble. Inferring these connections is often intractable because the set of possible interactions grows exponentially with ensemble size. This is a fundamental challenge one confronts when interpreting these data. Unfortunately, the combination of expert knowledge and ensemble data is often insufficient for selecting a unique model of these interactions. Our approach shifts away from modeling the network diagram of the ensemble toward analyzing changes in the dynamics of the ensemble as they relate to behavior. Our contribution consists of adapting techniques from signal processing and Bayesian statistics to track the dynamics of ensemble data on time-scales comparable with behavior. We employ a Bayesian estimator to weigh prior information against the available ensemble data, and use an adaptive quantization technique to aggregate poorly estimated regions of the ensemble data space. Importantly, our method is capable of detecting changes in both the magnitude and structure of correlations among neurons missed by firing rate metrics. We show that this method is scalable across a wide range of time-scales and ensemble sizes. Lastly, the performance of this method on both simulated and real ensemble data is used to demonstrate its utility

Information Bottleneck

The celebrated information bottleneck (IB) principle of Tishby et al. has recently enjoyed renewed attention due to its application in the area of deep learning. This collection investigates the IB principle in this new context. The individual chapters in this collection: • provide novel insights into the functional properties of the IB; • discuss the IB principle (and its derivates) as an objective for training multi-layer machine learning structures such as neural networks and decision trees; and • offer a new perspective on neural network learning via the lens of the IB framework. Our collection thus contributes to a better understanding of the IB principle specifically for deep learning and, more generally, of information–theoretic cost functions in machine learning. This paves the way toward explainable artificial intelligence

Automated Macro-scale Causal Hypothesis Formation Based on Micro-scale Observation

This book introduces new concepts at the intersection of machine learning, causal inference and philosophy of science: the macrovariable cause and effect. Methods for learning such from microvariable data are introduced. The learning process proposes a minimal number of guided experiments that recover the macrovariable cause from observational data. Mathematical definitions of a micro- and macro- scale manipulation, an observational and causal partition, and a subsidiary variable are given. These concepts provide a link to previous work in causal inference and machine learning. The main theoretical result is the Causal Coarsening Theorem, a new insight into the measure-theoretic structure of probability spaces and structural equation models. The theorem provides grounds for automatic causal hypothesis formation from data. Other results concern the minimality and sufficiency of representations created in accordance with the theorem. Finally, this book proposes the first algorithms for supervised and unsupervised causal macrovariable discovery. These algorithms bridge large-scale, multidimensional machine learning and causal inference. In an application to climate science, the algorithms re-discover a known causal mechanism as a viable causal hypothesis. In a psychophysical experiment, the algorithms learn to minimally change visual stimuli to achieve a desired effect on human perception.</p