How should I practice Binary Logistic Loss and Gradient?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Amazon phone screen problems in FastPrep.

Is Binary Logistic Loss and Gradient associated with Amazon?

FastPrep tags this as a Amazon phone screen coding practice problem when the problem catalog has that company and stage context.

Binary Logistic Loss and Gradient

Amazon● MediumFULLTIMEPHONE SCREEN

Learn

Problem statement

For this exercise, assume a batch of classification examples and the current parameters of a linear model. Implement its loss and analytic derivatives directly, without an automatic-differentiation or machine-learning library.

features is an n-by-d matrix; labels has one value per sample.

For sample i, let z[i] = bias + sum_j(features[i][j] * weights[j]) and p[i] = 1 / (1 + exp(-z[i])). The loss is mean binary cross-entropy: L = -sum_i(labels[i]*ln(p[i]) + (1-labels[i])*ln(1-p[i])) / n, using natural logarithms.

Return [L, dL/dweights[0], ..., dL/dweights[d-1], dL/dbias]. Differentiate with respect to the current weights and bias; do not update them. Compute the loss stably from logits, so a probability rounded to zero or one does not produce infinity.

No regularization, probability clipping or class weighting is used; labels are zero or one.

Function

binaryLossGradient(features: double[][], labels: int[], weights: double[], bias: double) → double[]

Examples

Example 1

features = [[1.0],[2.0]]labels = [0,1]weights = [0.0]bias = 0.0return = [0.6931471805599453,-0.25,0.0]

Both probabilities are 0.5. The mean loss is log(2), the weight derivative is -0.25 and the bias derivative is zero.

Example 2

features = [[0.0]]labels = [1]weights = [3.0]bias = 0.0return = [0.6931471805599453,0.0,-0.5]

Only the bias can change the zero-feature prediction. The result is log(2), zero weight derivative and -0.5 bias derivative.

Example 3

features = [[1.0]]labels = [0]weights = [0.0]bias = 1.0return = [1.3132616875182228,0.7310585786300049,0.7310585786300049]

The positive logit is 1. Loss is log(1+exp(1)); both parameter derivatives equal sigmoid(1).

Constraints

1 <= n <= 1000 and 1 <= d <= 50.
All arrays have the compatible shapes described above; all input numbers are finite.
Feature values, weights and bias are in [-10,10].
Labels are 0 or 1.
Each returned number is compared with absolute or relative tolerance 10^-6.
Use analytic derivatives; finite-difference estimates are outside the exercise contract.