Probability theory | Categorical data

In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth categorical data. Given a set of observation counts from a -dimensional multinomial distribution with trials, a "smoothed" version of the counts gives the estimator: where the smoothed count and the "pseudocount" α > 0 is a smoothing parameter. α = 0 corresponds to no smoothing. (This parameter is explained in below.) Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) , and the uniform probability . Invoking Laplace's rule of succession, some authors have argued that α should be 1 (in which case the term add-one smoothing is also used), though in practice a smaller value is typically chosen. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter α as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a Beta distribution as the conjugate prior for the parameters of Binomial distribution. (Wikipedia).

Least squares method for simple linear regression

In this video I show you how to derive the equations for the coefficients of the simple linear regression line. The least squares method for the simple linear regression line, requires the calculation of the intercept and the slope, commonly written as beta-sub-zero and beta-sub-one. Deriv

From playlist Machine learning

Frequency Domain Interpretation of Sampling

http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Analysis of the effect of sampling a continuous-time signal in the frequency domain through use of the Fourier transform.

From playlist Sampling and Reconstruction of Signals

11_3_1 The Gradient of a Multivariable Function

Using the partial derivatives of a multivariable function to construct its gradient vector.

From playlist Advanced Calculus / Multivariable Calculus

I discuss causal and non-causal noise filters: the moving average filter and the exponentially weighted moving average. I show how to do this filtering in Excel and Python

From playlist Discrete

Get a Free Trial: https://goo.gl/C2Y9A5 Get Pricing Info: https://goo.gl/kDvGHt Ready to Buy: https://goo.gl/vsIeA5 Learn how to smooth your signal using a moving average filter and Savitzky-Golay filter using Signal Processing Toolbox™. For more on Signal Processing Toolbox, visit: htt

From playlist Signal Processing and Communications

Practical DSP and Oversampling

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Limitations of analog anti-aliasing and anti-imaging filters motivate a practical digital filtering approach in which high rates are used for sampli

From playlist Sampling and Reconstruction of Signals

Reconstruction and the Sampling Theorem

http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Analysis of the conditions under which a continuous-time signal can be reconstructed from its samples, including ideal bandlimited interpolati

From playlist Sampling and Reconstruction of Signals

Arithmetic progressions and spectral structure - Thomas Bloom

Computer Science/Discrete Mathematics Seminar II Topic: Arithmetic progressions and spectral structure Speaker: Thomas Bloom Affiliation: University of Cambridge Date: October 13, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Data Science - Part X - Time Series Forecasting

For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of Time Series forecasting techniques and the process of creating effective for

From playlist Data Science

Pablo Shmerkin: Additive combinatorics methods in fractal geometry - lecture 3

In the last few years ideas from additive combinatorics were applied to problems in fractal geometry and led to progress on some classical problems, particularly on the smoothness of Bernoulli convolutions and other self-similar measures. We will introduce some of these tools from additive

From playlist Combinatorics

Statistical Learning: 7.4 Generalized Additive Models and Local Regression

Statistical Learning, featuring Deep Learning, Survival Analysis and Multiple Testing You are able to take Statistical Learning as an online course on EdX, and you are able to choose a verified path and get a certificate for its completion: https://www.edx.org/course/statistical-learning

From playlist Statistical Learning

Algebraic groups in positive characteristic - Srimathy Srinivasan

Short talks by postdoctoral members Topic: Algebraic groups in positive characteristic Speaker: Srimathy Srinivasan Affiliation: Member, School of Mathematics Date: October 4, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Edouard Pauwels: Curiosities and counterexamples in smooth convex optimization

CONFERENCE Recording during the thematic meeting : "Learning and Optimization in Luminy" the October 4, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C

From playlist Control Theory and Optimization

Martin J. Gander: Multigrid and Domain Decomposition: Similarities and Differences

Both multigrid and domain decomposition methods are so called optimal solvers for Laplace type problems, but how do they compare? I will start by showing in what sense these methods are optimal for the Laplace equation, which will reveal that while both multigrid and domain decomposition a

From playlist Numerical Analysis and Scientific Computing

Introduction to Frequency Selective Filtering

http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Separation of signals based on frequency content using lowpass, highpass, bandpass, etc filters. Filter g

From playlist Introduction to Filter Design

Battery Data Acquisition and Analysis Using MATLAB

Learn more on developing battery management systems: http://bit.ly/2P6Z6DA In this presentation, MathWorks engineers will demonstrate how to acquire and analyze battery discharge data using MATLAB. Get free resources on Battery Management systems: https://bit.ly/3ZnPqWi Download a trial

From playlist Power Electronics Control Design