Customize Consent Preferences

We use cookies to help you navigate efficiently and perform certain functions. You will find detailed information about all cookies under each consent category below.

The cookies that are categorized as "Necessary" are stored on your browser as they are essential for enabling the basic functionalities of the site. ... 

Always Active

Necessary cookies are required to enable the basic features of this site, such as providing secure log-in or adjusting your consent preferences. These cookies do not store any personally identifiable data.

No cookies to display.

Functional cookies help perform certain functionalities like sharing the content of the website on social media platforms, collecting feedback, and other third-party features.

No cookies to display.

Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics such as the number of visitors, bounce rate, traffic source, etc.

No cookies to display.

Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors.

No cookies to display.

Advertisement cookies are used to provide visitors with customized advertisements based on the pages you visited previously and to analyze the effectiveness of the ad campaigns.

No cookies to display.

Regressione lineare

Dato un insieme di dati vogliamo ottenere la miglior rappresentazione lineare che possa esprimere l’intero insieme di dati.

hW(x)=w1x+w0h_{\bf W}(x)=w_1\,x+w_0

Procediamo per passaggi:

  1. Troviamo i valori (w0,w1)(w_0,\,w_1) che minimizzano l’empirical loss
  2. Utilizzando come funzione di loss l’errore quadratico riusciamo a minimizzare tale errore nella funzione
    Loss(hW)=j=1NL2(yj,hW(xj))=j=1N(yjhW(xj))2=j=1N(yj(w1xj+w0))2 \begin{aligned} \text{Loss}(h_{\bf W})&=\sum_{j=1}^N L_2(y_j,\,h_{\bf W}(x_j))\\[10pt] &=\sum_{j=1}^N(y_j-h_{\bf W}(x_j))^2\\[10pt] &=\sum_{j=1}^N(y_j-(w_1\,x_j+w_0))^2 \end{aligned}

Nel caso in cui si abba a che fare con spazi di dimensione superiore a 22 bisognerà usare l’analogo 3D di questo algoritmo: il gradient descent.

Talvolta, le tecniche utilizzate nella regressione lineare possono essere sfruttate per tracciare i confini decisionali (decision boundaries) all’interno di un insieme di dati (che si assume essere divisibile linearmente, eventualmente in uno spazio Rn)\R^n)

Se hai trovato errori o informazioni mancanti scrivi a:
giacomo.dandria@esercizistem.com

Se hai trovato errori o informazioni mancanti scrivi a:
giacomo.dandria@esercizistem.com

Questa pagina è stata utile?
No
Torna in alto