Feature detection using spikes: the greedy approach

A goal of low-level neural processes is to build an efficient code extracting the relevant information from the sensory input. It is believed that this is implemented in cortical areas by elementary inferential computations dynamically extracting the most likely parameters corresponding to the sensory signal. We explore here a neuro-mimetic feed-forward model of the primary visual area (VI) solving this problem in the case where the signal may be described by a robust linear generative model. This model uses an over-complete dictionary of primitives which provides a distributed probabilistic representation of input features. Relying on an efficiency criterion, we derive an algorithm as an approximate solution which uses incremental greedy inference processes. This algorithm is similar to 'Matching Pursuit' and mimics the parallel architecture of neural computations. We propose here a simple implementation using a network of spiking integrate-and-fire neurons which communicate using lateral interactions. Numerical simulations show that this Sparse Spike Coding strategy provides an efficient model for representing visual data from a set of natural images. Even though it is simplistic, this transformation of spatial data into a spatio-temporal pattern of binary events provides an accurate description of some complex neural patterns observed in the spiking activity of biological neural networks.Comment: This work links Matching Pursuit with bayesian inference by providing the underlying hypotheses (linear model, uniform prior, gaussian noise model). A parallel with the parallel and event-based nature of neural computations is explored and we show application to modelling Primary Visual Cortex / image processsing. http://incm.cnrs-mrs.fr/perrinet/dynn/LaurentPerrinet/Publications/Perrinet04tau

Semantic Information G Theory and Logical Bayesian Inference for Machine Learning

An important problem with machine learning is that when label number n\u3e2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic

Adjusting Imperfect Data: Overview and Case Studies

Research users of large administrative have to adjust their data for quirks, problems, and issues that are inevitable when working with these kinds of datasets. Not all solutions to these problems are identical, and how they differ may affect how the data is to be interpreted. Some elements of the data, such as the unit of observation, remain fundamentally different, and it is important to keep that in mind when comparing data across countries. In this paper (written for Lazear and Shaw, 2007), we focus on the differences in the underlying data for a selection of country datasets. We describe two data elements that remain fundamentally different across countries -- the sampling or data collection methodology, and the basic unit of analysis (establishment or firm) -- and the extent to which they differ. We then proceed to document some of the problems that affect longitudinally linked administrative data in general, and we describe some of the solutions analysts and statistical agencies have implemented, and explore, through a select set of case studies, how each adjustment or absence thereof might affect the data.

Lossy compression of discrete sources via Viterbi algorithm

We present a new lossy compressor for discrete-valued sources. For coding a sequence $x^n$, the encoder starts by assigning a certain cost to each possible reconstruction sequence. It then finds the one that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor. The cost of each sequence is a linear combination of its distance from the sequence $x^n$ and a linear function of its $k^{\rm th}$ order empirical distribution. The structure of the cost function allows the encoder to employ the Viterbi algorithm to recover the minimizer of the cost. We identify a choice of the coefficients comprising the linear function of the empirical distribution used in the cost function which ensures that the algorithm universally achieves the optimum rate-distortion performance of any stationary ergodic source in the limit of large $n$, provided that $k$ diverges as $o(\log n)$. Iterative techniques for approximating the coefficients, which alleviate the computational burden of finding the optimal coefficients, are proposed and studied.Comment: 26 pages, 6 figures, Submitted to IEEE Transactions on Information Theor