Trevor Hastie Robert Tibshirani Jerome F Popular Books
Trevor Hastie Robert Tibshirani Jerome F Biography & Facts
In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used. Definition The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by L δ ( a ) = { 1 2 a 2 for | a | ≤ δ , δ ⋅ ( | a | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta \cdot \left(|a|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}} This function is quadratic for small values of a, and linear for large values, with equal values and slopes of the different sections at the two points where | a | = δ {\displaystyle |a|=\delta } . The variable a often refers to the residuals, that is to the difference between the observed and predicted values a = y − f ( x ) {\displaystyle a=y-f(x)} , so the former can be expanded to L δ ( y , f ( x ) ) = { 1 2 ( y − f ( x ) ) 2 for | y − f ( x ) | ≤ δ , δ ⋅ ( | y − f ( x ) | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(y,f(x))={\begin{cases}{\frac {1}{2}}(y-f(x))^{2}&{\text{for }}|y-f(x)|\leq \delta ,\\\delta \ \cdot \left(|y-f(x)|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}} The Huber loss is the convolution of the absolute value function with the rectangular function, scaled and translated. Thus it "smoothens out" the former's corner at the origin. Motivation Two very commonly used loss functions are the squared loss, L ( a ) = a 2 {\displaystyle L(a)=a^{2}} , and the absolute loss, L ( a ) = | a | {\displaystyle L(a)=|a|} . The squared loss function results in an arithmetic mean-unbiased estimator, and the absolute-value loss function results in a median-unbiased estimator (in the one-dimensional case, and a geometric median-unbiased estimator for the multi-dimensional case). The squared loss has the disadvantage that it has the tendency to be dominated by outliers—when summing over a set of a {\displaystyle a} 's (as in ∑ i = 1 n L ( a i ) {\textstyle \sum _{i=1}^{n}L(a_{i})} ), the sample mean is influenced too much by a few particularly large a {\displaystyle a} -values when the distribution is heavy tailed: in terms of estimation theory, the asymptotic relative efficiency of the mean is poor for heavy-tailed distributions. As defined above, the Huber loss function is strongly convex in a uniform neighborhood of its minimum a = 0 {\displaystyle a=0} ; at the boundary of this uniform neighborhood, the Huber loss function has a differentiable extension to an affine function at points .... Discover the Trevor Hastie Robert Tibshirani Jerome F popular books. Find the top 100 most popular Trevor Hastie Robert Tibshirani Jerome F books.
Best Seller Trevor Hastie Robert Tibshirani Jerome F Books of 2024
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Teach Me
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Think and Grow Rich
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Awaken Me
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The Wonderful Wizard of Oz
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Enemies With Benefits
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My Paper Heart
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A Christmas Carol
Charles DickensAn Apple Books Classic edition. It’s Christmas Eve in Victorian England. While some families don’t know where their next meal will come from, Ebenezer Scrooge sits in his large hom...
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The Honeymoon Homicide
J. R. Mathis & Susan MathisEnjoy this SmallTown Murder Mystery Featuring A Unique Sleuthing Couple I'm Father Tom Greer, a Catholic Priest in a smalltown parish who never expected this . . . When I came...
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Dream Psychology
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Pretty Little Lies
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His Girl Next Door
Khardine GrayFrom USA Today Bestselling author Khardine Gray comes a sizzling hot single dad romance you won't want to miss. No strings attached fun with the ubergorgeous single d...
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The Holy Bible - King James Version
King JamesHoly Bible King James Version Few Sample Paragraphs from The Holy Bible eBook, Genesis (OT) 1 Gen. 1 IN the beginning God created the heaven and the earth. 2 And the earth was with...
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Alpha
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You Are Kind
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Good Guy
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The Adventures of Sherlock Holmes
Arthur Conan DoyleAn Apple Books Classic You get not one, not two, but 25 gripping mysteries in Arthur Conan Doyle’s first of five collections of Sherlock Holmes short stories. Follow the brilliant ...
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Finding Cinderella
Colleen Hoover#1 New York Times bestselling author of It Starts with Us and It Ends With Us writes a free novella about the search for happily ever after. A chance encounter in the dark leads ei...
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The Great Gatsby
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The Icing on the Cake
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A Bookshop to Die For
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Get Lucky
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Silver Santa
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Law of Attraction
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Bewitching a Highlander
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Inception of Gold
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Christmas in Sweetbriar Cove
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Coffee Girl
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Saltwater Cove
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Once Upon A One-Night Stand
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Salvation
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The Art of War
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Become A Better Version of Yourself
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Meditations
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The Stoic Mind
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Whiskey Girl
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Little Women
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Dracula
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Teased by Fire
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Becoming Lady Dalton
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A Green Kind of Witch
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The Three Little Pigs
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The Cupcake Cottage
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Assisting the Bosshole
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Caught Up with the Captain
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Just Me
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Noxious
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The Count of Monte Cristo
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Always Yours
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Escape, A New Life
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Rogue Alpha
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