2 Kernel Regression
3 KR ad Alta performance
4 Studio di Fattibilità
Da: Dino [mailto:email@example.com] Inviato: giovedì 26 luglio 2001 19.09 A: Wolberg@hitech.technion.ac.il Oggetto: Question?
Dear Dr. Wolberg, regarding your „Expert Trading System“ book, which I had the pleasure to read, I will very grateful if you answer the following similar questions. Having calculated the j yˆ values in every single test point with a polynomial (order, dimensions, kernel, the three options), how could I make previsions for the future without knowing the future predictors values, but only the time?
How can I locate the future point in the p-Tree cells if I don’t know the future predictors value?
How can I significantly transpose the past values in the future if I can’t calculated the new polynomial coefficients? Thank you in advance. Sincerely,
Da: John Wolberg [mailto:firstname.lastname@example.org] Inviato: giovedì 26 luglio 2001 22.48 A: email@example.com Oggetto: Re: Question?
Dear Dino, The X values (i.e., the predictors are used to compute yˆ for the test points) must be defined so that they can be computed before the actual Y values are know.
So once you start using the system for making actual predictions, the same p-Tree is used in the same way that you used it to compute the yˆ values for the test points.
For time series work (like making stock market predictions) the X's are "backward looking" and the Y is a forward looking variable. For example, a typical X might be the fractional change over the last day and the Y might be the fraction change from today to tomorrow. I hope this clears up your problem. All the best... John Wolberg.
Da: John Wolberg [mailto:firstname.lastname@example.org] Inviato: giovedì 6 dicembre 2001 10.28 A: email@example.com Oggetto: Re: Some Questions! Hi Dino, here are some answers to your questions: Why in your Book do you consider only the exponential function about kernel? Is it better than others function?
Our experience has shown that the choice of kernel isn’t all that important for noisy problems like market modelling. In fact, most of our works uses fast mode which is just a 0 or 1 kernel (i.e., a point is either near enough to be used and thus gets a kernel of 1 or is excluded which is equivalent to getting a kernel value of 0). In earlier work that I did with kernel regression, we wrote code which allowed exponential kernels (i.e., exp(-K * D^2) where D is distance) and Cauchy kernels (i.e., 1 / (1 + K * D^2) which also has a value of 1 when D=0 and 0 when D is infinite).
We never found any significant reason for choosing one over the other so chose the exponential just because it is aesthetically more appealing. Is the p-Tree a "Classification Tree" or a "Regression Tree"? Which is the more appropriate name and Why? It is not a classification tree and I've never heard the word "Regression Tree". All it is a data structure that permits one to rapidly process the data by quickly discovering nearby neighbors. Use of this tree avoids the need to look at all points to discover nearby points. For large data sets this becomes crucial. I hope this answers your questions. All the best… John.
Kernel Regression Applicazione alla Previsione del Fib 30