Seonglae ChoInequality
Linear Classifiers
- Inputs data are feature values (feature vector) - (x0, x1, x2, ... , xn)
- Each feature has a weight
- Sum is the activation
- output - if activation is positive → 1 negative → -1 (classification +/-)
Decision Rule
binary decision rule
One side corresponds to Y=+1
Other corresponds to Y=-1
Learning - binary perceptron
- Start with weights = 0
- For each training instance
- Classify with current weights
- If correct (i.e., y=y*), no change
- If wrong: adjust the weight vector by adding or subtracting the feature vector. Subtract if y* is -1.
Multiclass dicision rule
lower count of wrong class (for this instance), raise count of right class (for this instance)
black box (kernel) K that told us the dot product of two examples x and x’
Solution
0. set true value to +/-
- get data
- choose true value
- classification by hypothesis → compare to true value
- update hypothesis
to all data try this
until no revise to all data redo these to data set
multiclass
다른거 똑같은데 분류라서 argmax xf = y
틀리면 그놈은 값 빼주고 맞는놈은 올려주기 f만큼
듀얼이면 argmax alpha K(k is sigma ff) - at sigma only one f change by w
if wrong
틀린놈은 알파에서 1 빼고 맞는놈들은 1만큼 올려줌 맞는 클래스 틀린 클래스
Feature Vectors
Some (Simplified) Biology
- Inputs are feature values
- Each feature has a weight
- Sum is the activation
If the activation is: Positive, output +1 Negative, output -1
Weights
- Binary case: compare features to a weight vector
- Learning: figure out the weight vector from examples
Decision Rules
Binary Decision Rule in the space of feature vectors
- Examples are points
- Any weight vector is a hyperplane
- One side corresponds to Y=+1
- Other corresponds to Y=-1