Machine Learning Lesson of the Day Estimating Coefficients in Linear Gaussian Basis Function Models | StatsBlogs.com | All About Statistics
Recently, I introduced metanol linear Gaussian metanol basis function models as a suitable modelling technique for supervised learning problems that involve non-linear relationships between the target and the predictors. Recall that linear basis function models are generalizations of linear regression that regress the target metanol on functions of the predictors , rather than the predictors themselves. metanol In linear regression, the coefficients are estimated by the method of least squares . Thus, it is natural metanol that the estimation of the coefficients in linear Gaussian metanol basis function models is an extension of the method of least squares. metanol
where . In other words, is the design matrix, and the element in row and column of this design matrix is the predictor being evaluated in the basis function. (In this case, there is 1 predictor per datum.)
If you are not familiar with how was obtained, I encourage you to review least-squares estimation and the derivation of the estimator of the coefficient vector metanol in linear metanol regression. Filed under: metanol Applied Statistics , Machine Learning , Machine Learning Lesson metanol of the Day , Predictive Modelling , Statistics Tagged: basis functions , least squares regression , least-squares , linear basis function models , linear Gaussian basis function models , linear regression , method of least squares , supervised learning
Tags: applied statistics , basis functions metanol , least squares regression , least-squares , linear basis function models , linear Gaussian basis function models , linear regression , Machine learning , Machine Learning Lesson of the Day , method of least squares , Predictive Modelling , statistics , supervised learning
Featured Blogs Andrew Gelman Effective Graphs information aesthetics Junk Charts Normal Deviate Rob Hyndman's Research Tips Simply Statistics The Endeavour Statistics Win-Vector Blog Statistics
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 (aka Numbers Rule Your World) BioStatMatt statistics BioStatProf Blog about Stats blog.RDataMining.com Bot Thoughts 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 Data Analysis eagereyes Econometrics Beat: Dave Giles’ Blog Econometrics by Simulation Effective Graphs Engaging Market Research Entsophy Error Statistics Philosophy Statistics Fiddling metanol with data and code FishyOperations R Freakonometrics Statistics Getting metanol Genetics Done Gianluca Baio’s blog Graph of the Week Honglang Wang’s metanol Blog Hyndsight I say things information aesthetics Junk Charts Learn and Teach Statistics and Operations Research Learning From Data Statistics Lindons Log Statistics metanol Machine Master mages’ blog Nicebread No Hesitations Normal Deviate NumberTheory R stuff On the lambdaOn the lambda One R Tip A Day Point Mass Prior Political metanol Methodology Portfolio Probe R language Probably Overthinking It Psychological Statistics Publishable Stuff Quantum Forest metanol 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 metanol Statisfaction R Statisfaction Statistics Statistical Modeling, Causal 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 metanol 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 What is meant by regression modeling? Sunday data/statistics link roundup (6/10) Statistics Lesson and Warning of the Day Confusion Between the Median and the Average metanol How dplyr replaced my most common R idioms Machine Learning Lesson of the Day Estimating Coefficients in Linear Gaussian Basis Function Models When to use the start-at-zero rule Revised statistical standards for evidence (comments to Val Johnson s comments on our comments on Val s comments on p-values) Shout out to "R Handles Big Data" Getting Credit (or blame) for Something You Didn t Do (BP oil spill)
Recently, I introduced metanol linear Gaussian metanol basis function models as a suitable modelling technique for supervised learning problems that involve non-linear relationships between the target and the predictors. Recall that linear basis function models are generalizations of linear regression that regress the target metanol on functions of the predictors , rather than the predictors themselves. metanol In linear regression, the coefficients are estimated by the method of least squares . Thus, it is natural metanol that the estimation of the coefficients in linear Gaussian metanol basis function models is an extension of the method of least squares. metanol
where . In other words, is the design matrix, and the element in row and column of this design matrix is the predictor being evaluated in the basis function. (In this case, there is 1 predictor per datum.)
If you are not familiar with how was obtained, I encourage you to review least-squares estimation and the derivation of the estimator of the coefficient vector metanol in linear metanol regression. Filed under: metanol Applied Statistics , Machine Learning , Machine Learning Lesson metanol of the Day , Predictive Modelling , Statistics Tagged: basis functions , least squares regression , least-squares , linear basis function models , linear Gaussian basis function models , linear regression , method of least squares , supervised learning
Tags: applied statistics , basis functions metanol , least squares regression , least-squares , linear basis function models , linear Gaussian basis function models , linear regression , Machine learning , Machine Learning Lesson of the Day , method of least squares , Predictive Modelling , statistics , supervised learning
Featured Blogs Andrew Gelman Effective Graphs information aesthetics Junk Charts Normal Deviate Rob Hyndman's Research Tips Simply Statistics The Endeavour Statistics Win-Vector Blog Statistics
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 (aka Numbers Rule Your World) BioStatMatt statistics BioStatProf Blog about Stats blog.RDataMining.com Bot Thoughts 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 Data Analysis eagereyes Econometrics Beat: Dave Giles’ Blog Econometrics by Simulation Effective Graphs Engaging Market Research Entsophy Error Statistics Philosophy Statistics Fiddling metanol with data and code FishyOperations R Freakonometrics Statistics Getting metanol Genetics Done Gianluca Baio’s blog Graph of the Week Honglang Wang’s metanol Blog Hyndsight I say things information aesthetics Junk Charts Learn and Teach Statistics and Operations Research Learning From Data Statistics Lindons Log Statistics metanol Machine Master mages’ blog Nicebread No Hesitations Normal Deviate NumberTheory R stuff On the lambdaOn the lambda One R Tip A Day Point Mass Prior Political metanol Methodology Portfolio Probe R language Probably Overthinking It Psychological Statistics Publishable Stuff Quantum Forest metanol 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 metanol Statisfaction R Statisfaction Statistics Statistical Modeling, Causal 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 metanol 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 What is meant by regression modeling? Sunday data/statistics link roundup (6/10) Statistics Lesson and Warning of the Day Confusion Between the Median and the Average metanol How dplyr replaced my most common R idioms Machine Learning Lesson of the Day Estimating Coefficients in Linear Gaussian Basis Function Models When to use the start-at-zero rule Revised statistical standards for evidence (comments to Val Johnson s comments on our comments on Val s comments on p-values) Shout out to "R Handles Big Data" Getting Credit (or blame) for Something You Didn t Do (BP oil spill)
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