Entropy def11/16/2023 ![]() For now this assumes `pmf` arrives as a well-formed distribution (that is, `np.sum(pmf)=1` and `not np.any(pmf 0`. For a totally deterministic distribution, where samples are always found in the same bin, then samples from the distribution give no more information and the entropy is 0. This is a measure of information in the distribution. Section 3.2: Calculating entropy from pmfīonus Section 1: The foundations for Entropyĭef entropy ( pmf ): """Given a discrete distribution, return the Shannon entropy in bits. Section 3.1: Computing probabilities from histogramĬoding Exercise 3.1: Probability Mass Function Section 3: Calculate entropy of ISI distributions from data Video 2: Entropy of different distributions Section 2: Information, neurons, and spikes Tutorial 3: Simultaneous fitting/regressionĮxample Model Project: the Train Illusion Tutorial 4: Model-Based Reinforcement Learning Tutorial 2: Learning to Act: Multi-Armed Bandits Tutorial 2: Optimal Control for Continuous State Tutorial 1: Optimal Control for Discrete States Tutorial 1: Sequential Probability Ratio Testīonus Tutorial 4: The Kalman Filter, part 2īonus Tutorial 5: Expectation Maximization for spiking neurons ![]() Tutorial 2: Bayesian inference and decisions with continuous hidden state Tutorial 1: Bayes with a binary hidden state Tutorial 3: Synaptic transmission - Models of static and dynamic synapsesīonus Tutorial: Spike-timing dependent plasticity (STDP)īonus Tutorial: Extending the Wilson-Cowan Model Tutorial 1: The Leaky Integrate-and-Fire (LIF) Neuron Model Tutorial 3: Combining determinism and stochasticity Tutorial 3: Building and Evaluating Normative Encoding Modelsīonus Tutorial: Diving Deeper into Decoding & Encoding Tutorial 2: Convolutional Neural Networks Tutorial 4: Nonlinear Dimensionality Reduction Tutorial 3: Dimensionality Reduction & Reconstruction Tutorial 6: Model Selection: Cross-validation Tutorial 5: Model Selection: Bias-variance trade-off Tutorial 4: Multiple linear regression and polynomial regression Tutorial 3: Confidence intervals and bootstrapping Tutorial 1: Differentiation and Integration Prerequisites and preparatory materials for NMA Computational Neuroscienceīonus Tutorial: Discrete Dynamical Systems The embedded matrix :math:`Y` is created by. It is clear that :math:`0 ≤ H (n) ≤ \\log_2(n!)` where the lower bound is attained for an increasing or decreasing sequence of values, and the upper bound for a completely random system where all :math:`n!` possible permutations appear with the same probability. This is the information contained in comparing :math:`n` consecutive values of the time series. math:: H = -\\sum p(\\pi)\\log_2(\\pi) where the sum runs over all :math:`n!` permutations :math:`\\pi` of order :math:`n`. ![]() The permutation entropy of a signal :math:`x` is defined as. Notes - The permutation entropy is a complexity measure for time-series first introduced by Bandt and Pompe in 2002. Returns - pe : float Permutation Entropy. Otherwise, return the permutation entropy in bit. normalize : bool If True, divide by log2(order!) to normalize the entropy between 0 and 1. ), AntroPy will calculate the average permutation entropy across all these delays. delay : int, list, np.ndarray or range Time delay (lag). Parameters - x : list or np.array One-dimensional time series of shape (n_times) order : int Order of permutation entropy. ![]() Def perm_entropy ( x, order = 3, delay = 1, normalize = False ): """Permutation Entropy. ![]()
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