Consider linear regression where y is our label vector, X is our data matrix, w is our model weights and o² is a measure of variance Using the squared error cost function has a probabilistic interpretation as: Maximising the probability of the model predicting the input data, assuming our input data follows a Normal distribution N(X; Xw, 0²) Maximising the probability of the model predicting the input data given the weights N(X; wy, o²) O Minimising the probability of the model predicting the labels, assuming our prediction errors follow a Normal distribution N(y; Xw, o²) Maximising the values of the weights to minimise the input data N (y; w, σ²) Maximising the probability of the model predicting the labels, assuming our prediction errors follow a Normal distribution N(y; Xw, 0²)

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Consider linear regression where y is our label vector, X is our data matrix, w is our model weights
and o² is a measure of variance
Using the squared error cost function has a probabilistic interpretation as:
O
O
O
Maximising the probability of the model predicting the input data, assuming our input data follows a Normal
distribution N(X; Xw, o²)
Maximising the probability of the model predicting the input data given the weights N(X; wy, o²)
Minimising the probability of the model predicting the labels, assuming our prediction errors follow a Normal
distribution N(y; Xw, o²)
Maximising the values of the weights to minimise the input data N (y; w, o²)
Maximising the probability of the model predicting the labels, assuming our prediction errors follow a
Normal distribution N(y; Xw, o²)
Transcribed Image Text:Consider linear regression where y is our label vector, X is our data matrix, w is our model weights and o² is a measure of variance Using the squared error cost function has a probabilistic interpretation as: O O O Maximising the probability of the model predicting the input data, assuming our input data follows a Normal distribution N(X; Xw, o²) Maximising the probability of the model predicting the input data given the weights N(X; wy, o²) Minimising the probability of the model predicting the labels, assuming our prediction errors follow a Normal distribution N(y; Xw, o²) Maximising the values of the weights to minimise the input data N (y; w, o²) Maximising the probability of the model predicting the labels, assuming our prediction errors follow a Normal distribution N(y; Xw, o²)
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