समस्या
Logistic regression is a linear model for yes/no questions. For each sample it computes a probability and turns it into a class:
- z = x₁×w₁ + … + xₙ×wₙ + bias
- p = 1 / (1 + e^(-z))
- class = 1 if p ≥ threshold, otherwise 0
Implement logistic_predict(samples, weights, bias, threshold).
Input
samples: One row of n features per sample.
weights: n weights.
bias: The bias.
threshold: The probability needed to predict class 1 (strictly between 0 and 1).
Output
Return the predicted class (0 or 1) of each sample, in order.
सीमाएँ
1 ≤ samples ≤ 1,000, 1 ≤ n ≤ 50
-100 ≤ each feature, weight and bias ≤ 100
0 < threshold < 1
उदाहरण
इनपुट:
bias = -1.0
samples = [
[2.0, 1.0],
[0.0, 0.0],
[-1.0, -3.0]
]
weights = [1.5, -0.5]
threshold = 0.5
अपेक्षित आउटपुट:
expected = [1, 0, 0]इनपुट:
double bias = -1.0;
std::vector<std::vector<double>> samples = {
{2.0, 1.0},
{0.0, 0.0},
{-1.0, -3.0}
};
std::vector<double> weights = {1.5, -0.5};
double threshold = 0.5;
अपेक्षित आउटपुट:
std::vector<long long> expected = {1, 0, 0};इनपुट:
double bias = -1.0;
double[][] samples = new double[][] {
new double[] {2.0, 1.0},
new double[] {0.0, 0.0},
new double[] {-1.0, -3.0}
};
double[] weights = new double[] {1.5, -0.5};
double threshold = 0.5;
अपेक्षित आउटपुट:
long[] expected = new long[] {1, 0, 0};व्याख्या
Sample 1: z = 3 - 0.5 - 1 = 1.5, p ≈ 0.818 → 1. Sample 2: z = -1, p ≈ 0.269 → 0. Sample 3: z = -1.5 + 1.5 - 1 = -1, p ≈ 0.269 → 0. Result: [1, 0, 0].
इनपुट:
bias = -2.0
samples = [
[1.0],
[2.0],
[3.0]
]
weights = [1.0]
threshold = 0.7
अपेक्षित आउटपुट:
expected = [0, 0, 1]इनपुट:
double bias = -2.0;
std::vector<std::vector<double>> samples = {
{1.0},
{2.0},
{3.0}
};
std::vector<double> weights = {1.0};
double threshold = 0.7;
अपेक्षित आउटपुट:
std::vector<long long> expected = {0, 0, 1};इनपुट:
double bias = -2.0;
double[][] samples = new double[][] {
new double[] {1.0},
new double[] {2.0},
new double[] {3.0}
};
double[] weights = new double[] {1.0};
double threshold = 0.7;
अपेक्षित आउटपुट:
long[] expected = new long[] {0, 0, 1};व्याख्या
The probabilities are σ(-1) ≈ 0.269, σ(0) = 0.5 and σ(1) ≈ 0.731. Only the last one reaches the 0.7 threshold, so the result is [0, 0, 1].
संदर्भ
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