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Lecture

Modeling Neurobiological Signals: Spikes & Firing Rate

In course

COM-500: Statistical signal and data processing through applications

Building up on the basic concepts of sampling, filtering and Fourier transforms, we address stochastic modeling, spectral analysis, estimation and prediction, classification, and adaptive filtering, with an application oriented approach and hands-on numeri ...

Description

This lecture covers the modeling of neurobiological signals, focusing on neurobiological spikes and firing rate. It explains how the activity of a neuron can be measured by its average firing rate and how spikes can be associated with a Poisson process. The lecture also delves into multiple state neurons, where firing rates change over time and can be modeled as piecewise constant. Additionally, it discusses parameter estimation for Markov chains and the modeling of samples generated by different classes using mixture models.

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Instructor

Andrea Ridolfi

I am a professor of Signal Processing and Communication Technologies at Bern University of Applied Sciences. Since 2004 I hold a lecturer position at EPFL, teaching “Mathematical Principles of Signal Processing” (Doctoral School, 2004 – 2011), “Statistical Signal and Data Processing through Applications” (Master Program, (2004 – ongoing), and Signal Processing and Machine Learning for Digital Humanities (Master, 2017 – 2019, co-taught with Mathieu Salzmann). Previously, I have been working as Project Manager and R&D Engineer at EPFL (2011-2014), coordinating the LCAV activities within the NSF – Nanotera project Opensense, and as Project Manager and R&D Engineer with the biomedical signal processing group at CSEM (2006-2011).

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Related concepts (32)

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Principal component analysis

Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data.

Mixture model

In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population.

Kernel principal component analysis

In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space. Recall that conventional PCA operates on zero-centered data; that is, where is one of the multivariate observations.

Markov chain

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).

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