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14,700 | the aalgorithm finds an optimal solution in this example because it gives up on two paths that are getting too long according to the heuristic plus total cost so far of course the optimality of the solution depends on the heuristic and the total cost for instancethe heuristic should be good enough to return as the cost... |
14,701 | heuristic search fig the connect four game algorithm the base cases for minimax are then modified as follows to incorporate the search cutoff heuristic the current board is win for the computer in that case minimax returns for computer win the current board is win for the human in that case minimax returns - for human ... |
14,702 | we have developed connect four implementation based on these ideas that runs on standard hardware without any special multiprocessing our version beats all commercially available apps and applications presently available when playing against them your challengeshould you care to take it onis to build better one front-e... |
14,703 | heuristic search will the best first search algorithm find an optimal solutionwhy or why not will the aalgorithm find an optimal solutionwhy or why not when would hill climbing be better to use than the aalgorithm what is forward checking and how does that help solve problem describe what happens in the depth first sea... |
14,704 | python version and common lisp installed both the front-end code and the author' back-end code must be in the same directory or folder to run the author' version of the program you can get the author' front-end and back-end code from the text' website this copy belongs to 'acha |
14,705 | this documentation was generated from the python documentation available by typing help(intin the python shell in this documentation the variables xyand refer to integers the official python documentation is at operator + - * / // % returns int int int float int int - & | xy << int int int int int >> ~ int int abs(xdiv... |
14,706 | this documentation was generated from the python documentation available by typing help(floatin the python shell in this documentation at least one of the variables and refer to floats the official python documentation is at python org/ operator + - * / // returns float float float float float % float abs(xdivmod(xyint... |
14,707 | methods this documentation was generated from the python documentation available by typing help(strin the python shell in the documentation found here the variables and are references to strings the official python documentation is at python org/ method + in == returns str bool bool >= <= > < != [ibool bool bool bool b... |
14,708 | appendix cstring operators and methods (continuedmethod center(width[fillchar]returns str count(sub[start[end]]int encode([encoding[errors]]bytes endswith(suffix[start[end]]bool expandtabs([tabsize]str find(sub[start[end]]int format(*args**kwargss index(sub[start[end]]str int isalnum(bool isalpha(bool isdecimal(bool is... |
14,709 | (continuedmethod isnumeric(returns bool isprintable(bool isspace(bool istitle(bool isupper(bool join(sequencestr ljust(width[fillchar]str lower( lstrip([chars]str str partition(sep( ,sep,ts replace (oldnew[count]str rfind(sub[start[end]]int rindex(sub[start[end]]int rjust(width[fillchar]str rpartition(sep( ,sep, commen... |
14,710 | appendix cstring operators and methods (continuedmethod rsplit([sep[maxsplit]]returns comments string list returns list of the words in susing sep as the delimiter stringstarting at the end of the string and working to the front if maxsplit is givenat most maxsplit splits are done if sep is not specifiedany whitespace ... |
14,711 | methods this documentation was generated from the python documentation available by typing help(listin the python shell in the documentation found here the variables and are references to lists the official python documentation is at method list(returns list list(sequenceitem [,item]list list + list in del [ibool == bo... |
14,712 | (continuedmethod [[ ]:[ ] appendix dlist operators and methods returns list [ ]= += *= iter(xlen(xx* * repr(xx append(eiterator int list list str none count(ex extend(iterx index( ,[ ,[ ]]int none int insert(iex pop([index]none item remove(enone reverse( sort(none none comments returns the slice of items starting at in... |
14,713 | methods this documentation was generated from the python documentation available by typing help(dictin the python shell in the documentation found here the variable is reference to dictionary few methods were omitted here for brevity the official python documentation is at method dict(dict(mappingdict(seqreturns dict d... |
14,714 | appendix edictionary operators and methods (continuedmethod keys( pop( [, ]returns keys popitem((kvd setdefault( [, ] update( **fd get( ,enone values(values comments set-like object providing view on ' keys remove specified key and return the corresponding value if key is not founde is returned if givenotherwise keyerr... |
14,715 | this documentation was generated from the python documentation available by typing from turtle import help turtle in the python shell in the documentation found here the variable turtle is reference to turtle object this is subset of that documentation the official python documentation is at method description turtle b... |
14,716 | appendix fturtle methods method description turtle begin_poly(start recording the vertices of polygon current turtle position is first point of polygon example (for turtle instance named turtle)turtle begin_poly(turtle circle(radiusextent=nonesteps=noneargumentsradius number extent (optionala number steps (optionalan i... |
14,717 | method description color(colorstring)color(( , , ))color( , ,binputs as in pencolorset bothfillcolor and pencolorto the given value color(colorstring colorstring )color(( , , )( , , )equivalent to pencolor(colorstring and fillcolor(colorstring and analogouslyif the other input format is used if turtleshape is polygonou... |
14,718 | appendix fturtle methods method description turtle end_poly(stop recording the vertices of polygon current turtle position is last point of polygon this will be connected with the first point example (for turtle instance named turtle)turtle end_poly(turtle filling(return fillstate (true if fillingfalse elseexample (for... |
14,719 | method description move the turtle forward by the specified distancein the direction the turtle is headed example (for turtle instance named turtle)turtle position(( turtle forward( turtle position(( , turtle forward(- turtle position((- , turtle get_poly(return the lastly recorded polygon example (for turtle instance ... |
14,720 | appendix fturtle methods method description example (for turtle instance named turtle)tp turtle pos(tp ( turtle setpos( , turtle pos(( , turtle setpos(( , )turtle pos(( , turtle setpos(tpturtle pos(( , turtle heading(return the turtle' current heading example (for turtle instance named turtle)turtle left( turtle headin... |
14,721 | method description turtle left(anglealiaseslt argumentangle number (integer or floatturn turtle left by angle units (units are by default degreesbut can be set via the degrees(and radians(functions angle orientation depends on mode (see this example (for turtle instance named turtle)turtle heading( turtle left( turtle ... |
14,722 | appendix fturtle methods method description turtle onrelease(funbtn= add=nonebind fun to mouse-button-release event on this turtle on canvas argumentsfun function with two argumentsto which will be assigned the coordinates of the clicked point on the canvas num number of the mouse-button defaults to (left mouse buttont... |
14,723 | method description set the line thickness to width or return it if resizemode is set to "autoand turtleshape is polygonthat polygon is drawn with the same line thickness if no argument is givencurrent pensize is returned example (for turtle instance named turtle)turtle pensize( turtle pensize( from here on lines of wid... |
14,724 | appendix fturtle methods method description standard modelogo-mode east north north east west south south west example (for turtle instance named turtle)turtle setheading( turtle heading( turtle shape(name=noneset turtle shape to shape with given name return current shapename optional argumentname stringwhich is valid ... |
14,725 | method description turtle undo(undo (repeatedlythe last turtle action number of available undo actions is determined by the size of the undobuffer example (for turtle instance named turtle)for in range( )turtle fd( )turtle lt( for in range( )turtle undo(turtle write(argmove=falsealign='left'font=('arial' 'normal')write... |
14,726 | this documentation was generated from the python documentation available by typing from turtle import help turtlescreenin the python shell in the documentation found here the variable turtle is reference to turtle object and screen is reference to the turtlescreen object this is subset of that documentation the officia... |
14,727 | appendix gturtlescreen methods method description screen bgpic(picname=noneset background image or return name of current backgroundimage optional argumentpicname stringname of gif-file or "nopicif picname is filenameset the corresponing image as background if picname is "nopic"delete backgroundimageif present if picna... |
14,728 | method description screen getcanvas(return the canvas of this turtlescreen example (for screen instance named screen)cv screen getcanvas(cv screen getshapes(return list of names of all currently available turtle shapes example (for turtlescreen instance named screen)screen getshapes(['arrow''blank''circle''turtle'scree... |
14,729 | appendix gturtlescreen methods method description screen onclick(funbtn= add=nonebind fun to mouse-click event on canvas argumentsfun function with two argumentsthe coordinates of the clicked point on the canvas num the number of the mouse-buttondefaults to example (for turtlescreen instance named screen and turtle ins... |
14,730 | method description screen onkeypress(funkey=nonebind fun to key-press event of key if key is givenor to any key-press-event if no key is given argumentsfun function with no arguments key stringkey ( " "or key-symbol ( "space"in order to be able to register key-eventsturtlescreen must have focus (see method listen examp... |
14,731 | appendix gturtlescreen methods method description screen register_shape(nameshape=noneadds turtle shape to turtlescreen' shapelist arguments( name is the name of gif-file and shape is none installs the corresponding image shape !image-shapes do not rotate when turning the turtle!so they do not display the heading of th... |
14,732 | method description screen setworldcoordinates(llxllyurxuryset up user defined coordinate-system argumentsllx numberx-coordinate of lower left corner of canvas lly numbery-coordinate of lower left corner of canvas urx numberx-coordinate of upper right corner of canvas ury numbery-coordinate of upper right corner of canv... |
14,733 | appendix gturtlescreen methods method description screen update(perform turtlescreen update screen window_height(return the height of the turtle window example (for turtlescreen instance named screen)screen window_height( screen window_width(return the width of the turtle window example (for turtlescreen instance named... |
14,734 | the draw program this is the sample drawing application from the first it illustrates the use of the tkinter library including many widgets and mouse handling this program can be downloaded from the text' website the and modules the and modules and import import import import import xml dom minidom the commands by goto... |
14,735 | appendix hcomplete programs color color def draw width width pencolor color turtle radius def '<command = width = width = beginfillcommand def color color def draw turtle color turtle begin_fill (def endfillcommand def pass def draw turtle end_fill (def penupcommand def pass def draw penup def penup pendowncommand def ... |
14,736 | def for in yield when on def return len the from frame means frame code which frame frame def =none super pack buildwindow graphicscommands method them gui and def buildwindow the window the draw below how menu the = means menus can be from window which menu menu bar code by new menu below when the same and below the m... |
14,737 | appendix hcomplete programs color color value cmd gotocommand width command = radius float radius value width width color color value cmd circlecommand width command = color color value cmd beginfillcommand command = cmd endfillcommand command =penup cmd penupcommand command =pendown cmd pendowncommand else unknown com... |
14,738 | update add_command load ,commanda dt the an xml def open "wf ' cmd graphicscommands ' cmdn write close def save as write filename add_command save as ,commands add_command ,commands add_cascade ,menuf window menu menub the on window canvas width = pack left by wt we can have draw on and same wt makes shape shape screen... |
14,739 | appendix hcomplete programs widthsize set radiuslabel label sidebar ext =radius pack gva radiusentry entry sidebar radiussize set pack an when the below when draw def when drawing command and command drawn by draw method dding command graphicscommands means remember cmd circlecommand cmd draw graphicscommands append cm... |
14,740 | def cmd beginfillcommand cmd draw graphicscommands append cmd commandb pack both def cmd endfillcommand cmd draw graphicscommands append cmd end commande pack both pen down pack def penuphandler cmd penupcommand cmd draw pen up graphicscommands append cmd penupbutton pen up command=penuphandler penupbutton pack both de... |
14,741 | appendix hcomplete programs cmd graphicscommands cmd draw update screen undohandler screen the main gui program window then which and has on makes the when def main tk drawingapp drawingapp mainloop program completed __name__ =__main__ main the scope program this is the sample program from the first that illustrates th... |
14,742 | float rstring val area print showoutput the __name__ =__main__ main import import import import import the sort animation tkinter turtle random time math wt def canvas super dot shape dot speed penup goto def return " xcor " ycor def return ycor other ycor the from frame frame def =none super pack buildwindow paused st... |
14,743 | appendix hcomplete programs et red penup goto pendown goto stop update + stop - while < while < and not seq += while < and seq -= if tmp seq seq seq seq goto seq seq tmp seq goto seq update += -= seq seq seq goto seq seq seq goto seq seq green update et white penup goto pendown goto seq update return def seq > return s... |
14,744 | math et blue penup goto ,- pendown et forward length update lst [ start mid merge two each has more while mid and seq seq append seq seq goto seq += else append seq seq goto seq += update copy mid while mid append seq seq goto seq += update copy mid while mid append seq seq goto seq += update copy back range seq goto g... |
14,745 | appendix hcomplete programs why once doesn seem some et red penup goto ,- pendown et forward length update seq mid stopping return seq mid stopping return et blue penup goto ,- pendown et forward length update merge seq mid update et white goto - ,- pendown et forward length + update def mergesort seq seq seq def seq m... |
14,746 | def paused pause stop pause running update screen return true return master animations menu menu bar def screen update screen def newwindow clear ( running stop true add_command ,command=newwindow add_command ,commands add_cascade ,menuf menub canvas width = pack left wt et ht speed screen et getscreen screen frame pad... |
14,747 | appendix hcomplete programs update screen range stopping return random , seq seq seq seq seq goto seq seq goto seq seq seq seq running stop commands pack both def running true clear ( , , width screen merge seq range stopping return point screen green seq append update screen range stopping return random , seq seq seq ... |
14,748 | clear ( , , , width screen master animation seq range stopping return point screen green seq append update screen range stopping return random , seq seq seq seq seq goto seq seq goto seq seq seq screen seq running stop commandq pack both def paused not paused pause commandp pack both def not paused and stop true stop c... |
14,749 | appendix hcomplete programs the plotdata program this is the plot program that is used throughout the text to plot experimentally gathered data so it can be visualized this program can be downloaded from the text' website import import import import import import import turtle tkinter colorchooser tkinter filedialog xm... |
14,750 | max( -round math max( -round math maxy minx - miny maxx maxy et ht penup goto minx miny pendown goto maxx miny penup goto minx miny pendown goto minx maxy penup goto miny , bold goto minx maxy , bold range minx miny penup goto minyy pendown goto miny- penup goto miny- % )% , normal penup goto minxx pendown goto minx- g... |
14,751 | appendix hcomplete programs for datapoint in datapoints datapoint float value float value goto dot update add_command load data ,commandl add_command ,commands add_cascade ,menuf menub canvas width = = pack left wt screen et getscreen screen none loadfile self datafile strip def main tk none len argv sys argv plotapp p... |
14,752 | can be copy board immutable from board def board=none =none screen screen =none board none board items range rowlst range board==none append (dummy else append board append method def return screen the method row board row board row column def return items index board row and column board can be method method two and s... |
14,753 | appendix hcomplete programs row range range row row row goto * + ,row * + update when no move has been made board when no move has been made dummy def pass def return def goto pass and below by the above then on wt wt def super ht , , , , , , , , , , , , , , , , , , , shape penup speed goto - ,- def computer wt def sup... |
14,754 | ct ct frame def =none super pack buildwindow paused stop running human locked false def buildwindow cv , , , , cv pack left wt cv screen getscreen screen ( screenmin screenmin screenmax screenmax screen bgcolor white ht frame frame frame pack right both board board none def screen screen ( screenmin screenmin screenmax... |
14,755 | appendix hcomplete programs def master frame commandq pack def computerturn the from making up mind locked true minimax move make reader you must complete code code maxmove move move row and column maxmove would be row maxmove board row cv locked false def not row col int board row cv computer board drawxos not board a... |
14,756 | the connect four front-end this provides the gui front-end to the connect four game presented in the last of the text this can serve as front-end for computer opponent back-end this program can be downloaded from the text' website import import import import import turtle subprocess tkinter sys time the program program... |
14,757 | appendix hcomplete programs ; draw format the game format computer human - wt def canvas row app super val row row col col app penup ht goto * + ,row * + def horc horc =computer shape else shape drop def getowner return def row def drop goto , screen speed self st goto * + row * + goto * + row * + goto * + row * + scre... |
14,758 | canvas width = pack left wt et ht screen et getscreen , , , screen register_shape blackchecker screen register_shape redchecker screen screen bgcolor yellow width range penup goto , pendown goto , et ht update def toother write \ toother fromother = messagebox game over won = messagebox game over you won = messagebox g... |
14,759 | appendix hcomplete programs row row row then we column was running true return row do human toother write \ toother toother write \ toother fromother print status is status row human update check game status checkstatus = do computer computerturn checkstatus running matrix range row range canvas row append append row u... |
14,760 | contents advantages and limitations of decision trees bootstrap aggregation random forests boosting exercises deep learning introduction feed-forward neural networks back-propagation methods for training steepest descent levenberg-marquardt method limited-memory bfgs method adaptive gradient methods examples in python ... |
14,761 | xi numerical root-finding and minimization newton-like methods quasi-newton methods normal approximation method nonlinear least squares constrained minimization via penalty functions probability and statistics random experiments and probability spaces random variables and probability distributions expectation joint dis... |
14,762 | xii pandas series and dataframe manipulating data frames extracting information plotting scikit-learn partitioning the data standardization fitting and prediction testing the model system callsurl accessand speed-up bibliography index |
14,763 | in our present world of automationcloud computingalgorithmsartificial intelligenceand big datafew topics are as relevant as data science and machine learning their recent popularity lies not only in their applicability to real-life questionsbut also in their natural blending of many different disciplinesincluding mathe... |
14,764 | keywords xvii preface backgroundas well as additional informationfrom linear algebra and functional analysis (appendix )multivariate differentiation and optimization (appendix )and probability and statistics (appendix cmoreoverto make the abstract ideas come alivewe believe it is important that the reader sees actual i... |
14,765 | xv in and explain the ideas behind broad class of regression models thereinwe also describe how python' statsmodels package can be used to define and analyze linear models builds upon the previous regression by developing the powerful concepts of kernel methods and regularizationwhich allow the fundamental ideas of to ... |
14,766 | we couldof courseuse any notation we wantdo not laugh at notationsinvent themthey are powerful in factmathematics isto large extentinvention of better notations richard feynman we have tried to use notation system that isin order of importancesimpledescriptiveconsistentand compatible with historical choices achieving a... |
14,767 | xviii we employ color to emphasize that certain words refer to datasetfunctionor package in python all code is written in typewriter font to be compatible with past notation choiceswe introduced special blue symbol for the model (designmatrix of linear model important notation such as ggis often defined in mnemonic way... |
14,768 | xix elementwise product intersection :==is defined as -converges almost surely to union - converges in distribution to -converges in probability to -converges in -norm to dxe smallest integer larger than xmax{ lp * bxc euclidean norm largest integer smaller than matrix/vector notation axtranspose of matrix or vector - ... |
14,769 | xx loss loss function ln (naturallogarithm set of natural numbers { big- order symbolf (xo( ( )if ( ) ag(xfor some constant as - little- order symbolf (xo( ( )if ( )/ ( as probability measure the number set of real numbers (one-dimensional euclidean spacern -dimensional euclidean space rpositive real line[ deterministi... |
14,770 | xxi kl kullback-leibler kkt karush-kuhn-tucker iid independent and identically distributed map maximum posteriori mcmc markov chain monte carlo mle maximum likelihood estimator/estimate oob out-of-bag pca principal component analysis pdf probability density function (discrete or continuoussvd singular value decompositi... |
14,771 | mporting ummarizing and isualizing data this describes where to find useful data setshow to load them into pythonand how to (re)structure the data we also discuss various ways in which the data can be summarized via tables and figures which type of plots and numerical summaries are appropriate depends on the type of th... |
14,772 | these data sets are typically stored in csv (comma separated valuesformatwhich can be easily read into python for exampleto access the abalone data set from this website with pythondownload the file to your working directoryimport the pandas package via import pandas as pd and read in the data as followsabalone pd read... |
14,773 | the data for each feature (corresponding to its specific namecan be accessed by using python' slicing notation [for examplethe object iris['sepal length'contains the sepal lengths the first three rows of the abalone data set from the uci repository can be found as followsabalone head ( herethe missing headers have been... |
14,774 | xls 'http :/www biostatisticien euspringer nutrition_elderly xls nutri pd read_excel (xlsthis creates dataframe object nutri the first three rows are as followspd set_option ('display max_columns ' to fit display nutri head ( gender situation tea cooked_fruit_veg chocol fat [ rows columns you can check the type (or str... |
14,775 | table description of the variables in the nutritional study [ feature gender situation tea coffee height weight age meat fish raw_fruit cooked_fruit_veg chocol fat unit or coding =male =female =single =living with spouse family status =living with family =living with someone else daily consumption of tea number of cups... |
14,776 | we can repeat this for the other variables (see exercise and save this modified data frame as csv fileby using the pandas method to_csv nutri to_csv ('nutri csv ',index false summary tables it is often useful to summarize large spreadsheet of data in more condensed form table of counts or table of frequencies makes it ... |
14,777 | it is also possible to use crosstab to cross tabulate between two or more variablesgiving contingency table cross tabulate pd crosstab nutri gender nutri situation situation gender female male couple family single we seefor examplethat the proportion of single men is substantially smaller than the proportion of single ... |
14,778 | sample range sample variance the sample mean and median give information about the location of the datawhile the distance between sample quantiles (say the and quantilesgives some indication of the dispersion (spreadof the data other measures for dispersion are the sample rangemaxi xi mini xi the sample variance (xi ) ... |
14,779 | for the rest of this sectionit is assumed that matplotlib pyplotpandasand numpyhave been imported in the python code as follows import matplotlib pyplot as plt import pandas as pd import numpy as np plotting qualitative variables suppose we wish to display graphically how many elderly people are living by themselvesas ... |
14,780 | boxplot boxplot boxplot can be viewed as graphical representation of the five-number summary of the data consisting of the minimummaximumand the firstsecondand third quartiles figure gives boxplot for the 'agefeature of the nutri data plt boxplot nutri ['age ']widths =width ,vertfalse plt xlabel ('age 'plt show (the wi... |
14,781 | here bins were used rather than using raw counts (the default)the vertical axis this is achieved by choosing the here gives the percentage in each classdefined by count total "weightsparameter to be equal to the vector with entries / with length various plotting parameters have also been changed proportion of total age... |
14,782 | fn( age figure plot of the empirical distribution function for the continuous quantitative feature 'agedata visualization in bivariate setting in this sectionwe present few useful visual aids to explore relationships between two features the graphical representation will depend on the type of the two features two-way p... |
14,783 | the figure was made using the seaborn packagewhich was specifically designed to simplify statistical visualization tasks import seaborn as sns sns countplot ( ='situation 'hue 'gender 'data=nutri hue_order ['male ''female ']palette ['skyblue ','pink ']saturation edgecolor ='black 'plt legend (loc='upper center 'plt xla... |
14,784 | urlprefix 'https :/vincentarelbundock github iordatasets /csv/dataname 'massbirthwt csv bwt pd read_csv urlprefix dataname bwt bwt drop('unnamed , #drop unnamed column styles { [' ','red '] ['^','blue ']for in styles grp bwt[bwt smoke ==km, np polyfit (grp age grp bwt fit straight line plt scatter (grp age grp bwt csty... |
14,785 | coffee male gender female figure boxplots of quantitative feature 'coffeeas function of the levels of categorical feature 'gendernote that we used different"notched"style boxplot this time further reading the focus in this book is on the mathematical and statistical analysis of dataand for the rest of the book we assum... |
14,786 | (dthe th column lists the various odors of the mushroomsencoded as ' '' 'replace these with the names 'almond''creosote'etc (categories corresponding to each letter can be found on the websitealso replace the 'edibilitycategories 'eand 'pwith 'edibleand 'poisonous(emake contingency table cross-tabulating 'edibilityand ... |
14,787 | (aload the data set into pandas dataframe object (busing matplotlib pyplotproduce boxplots of 'petal lengthfor each the three speciesin one figure (cmake histogram with bins for 'petal length(dproduce similar scatterplot for 'sepal lengthagainst 'petal lengthto that of the left plot in figure note that the points shoul... |
14,788 | dax smi cac ftse figure closing stock indices for various european stock markets consider the kasandr data set from the uci machine learning repositorywhich can be downloaded from tar bz this archive file has size of mbso it may take while to download uncompressing the file ( via -zipyields directory de containing two ... |
14,789 | tatistical earning the purpose of this is to introduce the reader to some common concepts and themes in statistical learning we discuss the difference between supervised and unsupervised learningand how we can assess the predictive performance of supervised learning we also examine the central role that the linear and ... |
14,790 | probability and statistics in generalthe data used to fit the model is viewed as realization of random process or numerical vectorwhose probability law determines the accuracy with which we can predict future observations thusin order to quantify the uncertainty inherent in making predictions about the futureand the so... |
14,791 | function is called classifier given the distribution of (xyand any loss functionwe can in principle find the best possible :argming loss(yg( )that yields the smallest risk `:`(gwe will see in that in the classification case with { - and `(gp[ ( )]we have classifier (xargmax ( ) { , - where ( xp[ xis the conditional pro... |
14,792 | learner supervised learning explanatory variables unsupervised learning supervised and unsupervised learning from note that gt is random function particular outcome is denoted by gt it is often useful to think of teacher-learner metaphorwhereby the function gt is learner who learns the unknown functional relationship g... |
14,793 | training and test loss given an arbitrary prediction function git is typically not possible to compute its risk `(gin ( howeverusing the training sample we can approximate `(gvia the empirical (sample averagerisk loss(yi (xi ))( ` (gn = which we call the training loss the training loss is thus an unbiased estimator of ... |
14,794 | figure the generalization risk for fixed training set is the weighted-average loss over all possible pairs (xyexpected generalization risk for random training set the generalization risk is thus random variable that depends on (and gif we average the generalization risk over all possible instances of we obtain the expe... |
14,795 | table summary of definitions for supervised learning (xyf ( xt or tn or tn loss( , `(gggg ` ( ` (gggt or gt ggt or gt fixed explanatory (featurevector random explanatory (featurevector fixed (real-valuedresponse random response joint pdf of and yevaluated at (xyconditional pdf of given xevaluated at fixed training data... |
14,796 | figure statistical learning algorithms often require the data to be divided into training and test data if the latter is used for model selectiona third set is needed for testing the performance of the selected model we next consider concrete example that illustrates the concepts intr... |
14,797 | to obtain good estimate of (ubased on the training set {(ui yi ) }we minimize the outcome of the training loss ( ) (yi (ui )) ` (hn = ( over suitable set of candidate functions let us take the set of polynomial functions in of order ( : - ( for and parameter vector [ ]this function class contains the best possible (ue[... |
14,798 | xb xb span(xfigure xb is the orthogonal projection of onto the linear space spanned by the columns of the matrix according to theorem the projection matrix is given by xpseudo-inverse normal equations where the matrix xin ( is the pseudo-inverse of if happens to be of full column rank (so that none of the columns can b... |
14,799 | we see that for the fitted curve lies closer to the data pointsbut is further away from the dashed true polynomial curveindicating that we overfit the choice (the true cubic polynomialis much better than or indeed (straight lineg each function class gives different learner gt to assess which is betterwe should not simp... |
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