Machine Learning Lesson of the Day Linear Gaussian thorgan hazard Basis Function Models | StatsBlogs.com | All About Statistics
I recently introduced the use of linear basis function models for supervised learning problems that involve non-linear relationships between the predictors and the target. A common type of basis function for such models is the Gaussian basis function . This type of model uses the kernel of the normal (or Gaussian) probability density function (PDF) as the basis function.
Notice that this is just the normal PDF without the scaling factor of ; the scaling factor ensures that the normal PDF integrates to 1 over its support set. In a linear basis function model, the regression coefficients are the weights for the basis functions, and these weights will scale Gaussian basis functions to fit the data that are local to . Thus, there is no need to include that scaling factor of , because the scaling is already being handled by the regression coefficients.
The Gaussian basis function model is useful because it can model many non-linear thorgan hazard relationships between the predictor and the target surprisingly well, each basis function is non-zero over a very small interval and is zero everywhere else. These local basis functions result in a very sparse design matrix (i.e. one with mostly zeros) that leads to much faster computation . Filed under: Machine Learning , Machine Learning Lesson of the Day , Predictive Modelling , Statistics thorgan hazard Tagged: Gaussian basis function models , Gaussian thorgan hazard distribution , Gaussian linear basis function models , linear basis function models , machine thorgan hazard learning , normal thorgan hazard distribution , normal PDF , statistics thorgan hazard
Tags: Gaussian basis function models , Gaussian distribution , Gaussian linear basis function models , linear basis function models , Machine learning , Machine Learning Lesson of the Day , normal distribution , normal PDF , Predictive Modelling , statistics
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Top Posts Add Your Blog Sunday data/statistics link roundup (6/10) Bayes's theorem and logistic regression Dave Giles on "MCMC for Econometrics Students" Past, present, and future of statistical science A bit of the agenda of Practical Data Science with R How much RAM do I need to store that matrix? Bayesian Uncertainty Quantification for Differential Equations! How dplyr replaced my most common R idioms A clear picture thorgan hazard of power and significance in A/B tests
I recently introduced the use of linear basis function models for supervised learning problems that involve non-linear relationships between the predictors and the target. A common type of basis function for such models is the Gaussian basis function . This type of model uses the kernel of the normal (or Gaussian) probability density function (PDF) as the basis function.
Notice that this is just the normal PDF without the scaling factor of ; the scaling factor ensures that the normal PDF integrates to 1 over its support set. In a linear basis function model, the regression coefficients are the weights for the basis functions, and these weights will scale Gaussian basis functions to fit the data that are local to . Thus, there is no need to include that scaling factor of , because the scaling is already being handled by the regression coefficients.
The Gaussian basis function model is useful because it can model many non-linear thorgan hazard relationships between the predictor and the target surprisingly well, each basis function is non-zero over a very small interval and is zero everywhere else. These local basis functions result in a very sparse design matrix (i.e. one with mostly zeros) that leads to much faster computation . Filed under: Machine Learning , Machine Learning Lesson of the Day , Predictive Modelling , Statistics thorgan hazard Tagged: Gaussian basis function models , Gaussian thorgan hazard distribution , Gaussian linear basis function models , linear basis function models , machine thorgan hazard learning , normal thorgan hazard distribution , normal PDF , statistics thorgan hazard
Tags: Gaussian basis function models , Gaussian distribution , Gaussian linear basis function models , linear basis function models , Machine learning , Machine Learning Lesson of the Day , normal distribution , normal PDF , Predictive Modelling , statistics
Featured Blogs Andrew thorgan hazard Gelman Effective Graphs information aesthetics thorgan hazard Junk Charts Normal Deviate Rob Hyndman's Research Tips Simply Statistics The Endeavour thorgan hazard Statistics Win-Vector Blog Statistics thorgan hazard
Contributing Blogs Access to Statistics Adventures in Analytics and Visualization Adventures in R All Things R Analysis with Programming analyze stuff Asymptotically Unbiased bayesianbiologist Rstats Big Data, Plainly Spoken thorgan hazard (aka Numbers Rule Your World) BioStatMatt statistics BioStatProf Blog about Stats blog.RDataMining.com Bot Thoughts thorgan hazard Burns Statistics Carlisle Rainey Methods/Statistics CoolStatsBlog dahtah Darren Wilkinson’s research blog Data Miners Blog Data Mining – Blog.com Data Mining: Text Mining, Visualization and Social Media Data, Evidence, and Policy – Jared Knowles DiffusePrioR Doing Bayesian thorgan hazard Data Analysis eagereyes Econometrics Beat: Dave Giles’ Blog Econometrics by Simulation Effective Graphs Engaging Market Research Entsophy Error Statistics Philosophy thorgan hazard Statistics Fiddling with data and code FishyOperations R Freakonometrics thorgan hazard Statistics Getting Genetics Done Gianluca Baio’s blog Graph of the Week Honglang Wang’s Blog Hyndsight I say things information aesthetics Junk Charts Learn and Teach Statistics and Operations Research Learning From Data Statistics Lindons thorgan hazard Log Statistics Machine Master mages’ blog Nicebread thorgan hazard No Hesitations Normal Deviate NumberTheory R stuff On the lambdaOn the lambda One R Tip A Day Point Mass Prior Political Methodology Portfolio Probe R language Probably Overthinking It Psychological Statistics Publishable Stuff Quantum Forest rblogs R Chronicle R snippets R Tutorial r4stats.com rbresearch R Realizations in Biostatistics SAS and R SAS Programming for Data Mining Serious Stats Sharp Statistics Simply Statistics Stat Bandit statalgo Statisfaction R Statisfaction Statistics Statistical Modeling, Causal thorgan hazard Inference, and Social Science Statistical Research Systematic Investor R The Analysis Factor The Chemical Statistician Statistics The Data Game – Ilan Man The DO Loop The Endeavour Statistics The R Trader The stupidest thing… R The stupidest thing… Statistics Three-Toed Sloth TRinker’s R Blog TRinker’s Stats Blog Vik Paruchuri Wiekvoet Will Lowe Win-Vector Blog Statistics Xi’an’s Og R Yihui Xie
Top Posts Add Your Blog Sunday data/statistics link roundup (6/10) Bayes's theorem and logistic regression Dave Giles on "MCMC for Econometrics Students" Past, present, and future of statistical science A bit of the agenda of Practical Data Science with R How much RAM do I need to store that matrix? Bayesian Uncertainty Quantification for Differential Equations! How dplyr replaced my most common R idioms A clear picture thorgan hazard of power and significance in A/B tests
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