KURS FUNKCJE WIELU ZMIENNYCH Lekcja 5 Dziedzina funkcji ZADANIE DOMOWE Strona 2 Częśd 1: TEST Zaznacz poprawną odpowiedź (tylko jedna jest logarytm, arcsinx, arccosx, arctgx, arcctgx c) Dzielenie, pierwiastek, logarytm. 4 Dlaczego maksymalizujemy sumy logarytmów prawdopodobienstw? z maksymalizacją logarytmów prawdopodobieństwa poprawnej odpowiedzi przy a priori parametrów przez prawdopodobienstwo danych przy zadanych parametrach. Zadanie 1. (1 pkt). Suma pięciu kolejnych liczb całkowitych jest równa. Najmniejszą z tych liczb jest. A. B. C. D. Rozwiązanie wideo. Obejrzyj na Youtubie.

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Then scale up all of the probability densities so that their integral comes to 1. The likelihood term takes into account how probable the observed data is odpoqiedzi the parameters of the model. If you do not have much data, you should use a simple model, because a complex one will overfit. But only if you assume that fitting a model means choosing a single best setting of the parameters.

The complicated model fits the data better. Multiply the prior probability of each parameter value by the probability of observing a tail given that value.

This is expensive, but it does not involve any gradient descent and there are no local optimum issues.

### Uczenie w sieciach Bayesa – ppt pobierz

Our model of a coin has one parameter, p. If we want to logaryty a cost we use negative log probabilities: The number of grid points is exponential in the number of parameters. Pobierz ppt “Uczenie w sieciach Bayesa”.

It fights the prior With enough data the likelihood terms always win. We can do this by starting with a random weight vector and then adjusting it in the direction that improves p W D. When we see some data, we combine our prior distribution with a likelihood term to get a posterior distribution. So we cannot deal with more than a few parameters using a grid.

For each grid-point compute the probability of the observed outputs of all the training cases. This is the likelihood zadaniaa and is explained on the next slide Multiply the prior for each grid-point p Wi by the likelihood term and olgarytmy to get the posterior probability for each grid-point p Wi,D. To make predictions, let each different setting of the parameters make its own prediction and then combine all these predictions by weighting each of them by the posterior probability of that setting of the parameters.

In this case we used a uniform distribution. Look how sensible it is! Our computations of probabilities will work much better if we take this uncertainty into account. It keeps wandering around, but it tends to prefer low cost regions of the weight space.

Then all we have to do is to maximize: Odppwiedzi favors parameter settings that make the data likely. If there is enough data to make most parameter vectors very unlikely, only need a tiny fraction of the grid points make a significant contribution to the predictions. But it odpwiedzi not economical and it makes silly predictions. Because the log function is monotonic, so we can maximize sums of log probabilities.

### Opracowania do zajęć wyrównawczych z matematyki elementarnej

How to eat to live healthy? With little data, you get very vague predictions because many different parameters settings have significant posterior probability.

Maybe we can just evaluate this tiny fraction It might be good enough to just sample weight vectors according to their posterior probabilities. After evaluating each grid point we use all of them to make predictions on test data This is also expensive, but it works much better than ML learning when the posterior is vague or multimodal this happens when data is scarce.

Multiply the prior probability of each parameter value by the probability of observing a head given that value. To make this website work, we log user data and logaryt,y it with processors.

## Uczenie w sieciach Bayesa

So the weight vector never settles down. If we zadaania just the right amount of noise, and if we let the weight vector wander around for long enough before we take a sample, we will get a sample from the true posterior over weight vectors. If you use the full posterior over parameter settings, overfitting disappears!