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Now consider the Perceptron algorithm with Offset. Whenever there is a mistake ( or equivalently, whenever y ^ ( i ) ( theta x
Now consider the Perceptron algorithm with Offset. Whenever there is a "mistake" or equivalently, whenever yitheta xitheta ie when the label yi and hx do not match perceptron updates theta with theta yi xi and theta with theta yi More formally, the Perceptron Algorithm with Offset is defined as follows: Perceptron xi yi i n T : initialize theta vector; theta scalar for t T do for i n do if yitheta xitheta then update theta theta yi xi update theta theta yi In the next set of problems, we will try to understand why such an update is a reasonable one. When a mistake is spotted, do the updated values of theta and theta provide a better prediction? In other words, is yitheta yi xi xitheta yi always greater than or equal to yitheta xitheta Yes, because theta yi xi is always larger than theta Yes, because yixiyi No because yixiyi No because theta yi xi is always larger than theta rn For a given example i we defined the training error as if yitheta xitheta and otherwise: epsi itheta theta yitheta xitheta Say we have a linear classifier given by theta theta After the perceptron update using example i the training error epsi itheta theta for that example can select all those apply: Increase Stay the same Decrease
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