slug stringlengths 6 37 | title stringlengths 9 61 | difficulty stringclasses 3
values | signature stringlengths 9 74 | starter_python stringlengths 83 190 | tests listlengths 4 10 | url stringlengths 37 68 |
|---|---|---|---|---|---|---|
ml-stable-softmax | Softmax that never overflows | Easy | softmax(x) | import numpy as np
def softmax(x):
# x: list of floats. Return a list (or 1-D array) of probabilities.
pass | [
{
"args": [
[
1,
2,
3
]
],
"out": [
0.0900305732,
0.2447284711,
0.6652409558
]
},
{
"args": [
[
0,
0,
0,
0
]
],
"out": [
0.25,
0.25,
0.25,
0.25
]
},
{
... | https://geodesicpartners.co.uk/ml-stable-softmax |
ml-cross-entropy-from-logits | Cross-entropy loss and its gradient from logits | Medium | cross_entropy(logits, labels) | import numpy as np
def cross_entropy(logits, labels):
# logits: N x C list of lists, labels: list of N ints.
# Return [loss, grad] with loss a float and grad an N x C list.
pass | [
{
"args": [
[
[
2,
1,
0
]
],
[
0
]
],
"out": [
0.4076059644,
[
[
-0.3347590442,
0.2447284711,
0.0900305732
]
]
]
},
{
"args": [
[
[
... | https://geodesicpartners.co.uk/ml-cross-entropy-from-logits |
ml-bce-with-logits | Binary cross-entropy from logits | Medium | bce_with_logits(z, y) | import numpy as np
def bce_with_logits(z, y):
# z: list of floats (logits), y: list of 0/1 labels. Return the mean loss as a float.
pass | [
{
"args": [
[
0
],
[
1
]
],
"out": 0.6931471806
},
{
"args": [
[
2,
-1
],
[
1,
0
]
],
"out": 0.2200948493
},
{
"args": [
[
-800
],
[
1
]
],
... | https://geodesicpartners.co.uk/ml-bce-with-logits |
ml-ridge-regression | Ridge regression in closed form | Easy | ridge(X, y, lam) | import numpy as np
def ridge(X, y, lam):
# X: n x d list of lists, y: list of n floats, lam: float >= 0.
# Return the d weights as a list.
pass | [
{
"args": [
[
[
1,
0
],
[
0,
1
],
[
1,
1
]
],
[
1,
2,
3
],
0
],
"out": [
1,
2
]
},
{
"args": [
[
[
... | https://geodesicpartners.co.uk/ml-ridge-regression |
ml-linear-regression-gradient-descent | Linear regression by gradient descent | Medium | fit_linear_gd(X, y, lr, steps) | import numpy as np
def fit_linear_gd(X, y, lr, steps):
# X: n x d, y: n targets. Return [w_1, ..., w_d, b].
pass | [
{
"args": [
[
[
1
],
[
2
],
[
3
]
],
[
2,
4,
6
],
0.1,
1
],
"out": [
1.8666666667,
0.8
]
},
{
"args": [
[
[
1
... | https://geodesicpartners.co.uk/ml-linear-regression-gradient-descent |
ml-logistic-regression | Logistic regression with an L2 penalty | Medium | fit_logistic(X, y, lr, steps, lam) | import numpy as np
def fit_logistic(X, y, lr, steps, lam):
# X: n x d, y: n labels in {0, 1}. Return [w_1, ..., w_d, b].
pass | [
{
"args": [
[
[
1
],
[
-1
]
],
[
1,
0
],
1,
1,
0
],
"out": [
0.5,
0
]
},
{
"args": [
[
[
0,
0
],
[
1,
... | https://geodesicpartners.co.uk/ml-logistic-regression |
ml-mlp-forward-pass | Forward pass of a two-layer network | Easy | mlp_forward(X, W1, b1, W2, b2) | import numpy as np
def mlp_forward(X, W1, b1, W2, b2):
# Return the N x C matrix of probabilities.
pass | [
{
"args": [
[
[
1,
2
]
],
[
[
1,
0
],
[
0,
1
]
],
[
0,
0
],
[
[
1,
0
],
[
0,
1
... | https://geodesicpartners.co.uk/ml-mlp-forward-pass |
ml-mlp-backpropagation | Backpropagation through a two-layer network | Hard | mlp_grads(X, y, W1, b1, W2, b2) | import numpy as np
def mlp_grads(X, y, W1, b1, W2, b2):
# Return [dW1, db1, dW2, db2], each with its parameter's shape.
pass | [
{
"args": [
[
[
1,
2
]
],
[
0
],
[
[
1,
0
],
[
0,
1
]
],
[
0,
0
],
[
[
1,
0
],
[
... | https://geodesicpartners.co.uk/ml-mlp-backpropagation |
ml-adam-optimizer | The Adam optimiser, with bias correction | Medium | adam(theta, grads, lr, beta1, beta2, eps) | import numpy as np
def adam(theta, grads, lr, beta1, beta2, eps):
# theta: list of floats; grads: list of gradient vectors, applied in order.
pass | [
{
"args": [
[
1
],
[
[
0.5
]
],
0.1,
0.9,
0.999,
1e-8
],
"out": [
0.9000000020000001
]
},
{
"args": [
[
1,
-2
],
[
[
100,
-0.001
]
... | https://geodesicpartners.co.uk/ml-adam-optimizer |
ml-inverted-dropout | Inverted dropout, forward and backward | Easy | dropout(X, mask, p, dout) | import numpy as np
def dropout(X, mask, p, dout):
# Return [out, dX].
pass | [
{
"args": [
[
[
1,
2
],
[
3,
4
]
],
[
[
1,
0
],
[
1,
1
]
],
0.5,
[
[
1,
1
],
[
... | https://geodesicpartners.co.uk/ml-inverted-dropout |
ml-gradient-clipping | Gradient clipping by global norm | Easy | clip_grad_norm(grads, max_norm) | import numpy as np
def clip_grad_norm(grads, max_norm):
# grads: list of arrays of any shape. Return [clipped_grads, total_norm].
pass | [
{
"args": [
[
[
3
],
[
4
]
],
1
],
"out": [
[
[
0.59999988
],
[
0.79999984
]
],
5
]
},
{
"args": [
[
[
0.1,
0.2
... | https://geodesicpartners.co.uk/ml-gradient-clipping |
ml-learning-rate-schedule | Linear warm-up with cosine decay | Easy | lr_schedule(steps, base_lr, min_lr, warmup, total) | import math
def lr_schedule(steps, base_lr, min_lr, warmup, total):
# Return the learning rate for each step, as a list.
pass | [
{
"args": [
[
0,
1,
2,
3
],
1,
0,
4,
10
],
"out": [
0.25,
0.5,
0.75,
1
]
},
{
"args": [
[
4,
7,
10
],
1,
0,
4,
10
],
"out": [
... | https://geodesicpartners.co.uk/ml-learning-rate-schedule |
ml-layer-normalization | Layer normalisation | Easy | layer_norm(X, gamma, beta, eps) | import numpy as np
def layer_norm(X, gamma, beta, eps):
# X: N x D. Normalise each row over its D features.
pass | [
{
"args": [
[
[
1,
2,
3
]
],
[
1,
1,
1
],
[
0,
0,
0
],
0
],
"out": [
[
-1.2247448714,
0,
1.2247448714
]
]
},
{
"args": [... | https://geodesicpartners.co.uk/ml-layer-normalization |
ml-batch-normalization | Batch normalisation in training mode | Medium | batch_norm_train(X, gamma, beta, running_mean, running_var, momentum, eps) | import numpy as np
def batch_norm_train(X, gamma, beta, running_mean, running_var, momentum, eps):
# Return [out, new_running_mean, new_running_var].
pass | [
{
"args": [
[
[
1,
10
],
[
3,
30
]
],
[
1,
1
],
[
0,
0
],
[
0,
0
],
[
1,
1
],
0.1,
0
],
"out": [... | https://geodesicpartners.co.uk/ml-batch-normalization |
ml-scaled-dot-product-attention | Scaled dot-product attention with a causal mask | Medium | attention(Q, K, V, causal) | import numpy as np
def attention(Q, K, V, causal):
# Q: n x d, K: m x d, V: m x dv, causal: bool. Return n x dv.
pass | [
{
"args": [
[
[
1,
0
]
],
[
[
1,
0
],
[
0,
1
]
],
[
[
10,
0
],
[
0,
10
]
],
false
],
... | https://geodesicpartners.co.uk/ml-scaled-dot-product-attention |
ml-conv2d | 2-D convolution with stride and padding | Medium | conv2d(image, kernel, stride, padding) | import numpy as np
def conv2d(image, kernel, stride, padding):
# Cross-correlation with zero padding and stride. Return a 2-D list or array.
pass | [
{
"args": [
[
[
1,
2,
3
],
[
4,
5,
6
],
[
7,
8,
9
]
],
[
[
1,
0
],
[
0,
-1
]
]... | https://geodesicpartners.co.uk/ml-conv2d |
ml-lstm-cell | One step of an LSTM cell | Medium | lstm_cell(x, h, c, W, b) | import numpy as np
def lstm_cell(x, h, c, W, b):
# Return [h_new, c_new] as lists.
pass | [
{
"args": [
[
1
],
[
0
],
[
0
],
[
[
0.5,
0
],
[
0.5,
0
],
[
1,
0
],
[
1,
0
]
],
[
... | https://geodesicpartners.co.uk/ml-lstm-cell |
ml-gru-cell | One step of a GRU cell, as PyTorch computes it | Medium | gru_cell(x, h, W_ih, W_hh, b_ih, b_hh) | import numpy as np
def gru_cell(x, h, W_ih, W_hh, b_ih, b_hh):
# Return h_new as a list.
pass | [
{
"args": [
[
1
],
[
0
],
[
[
1
],
[
1
],
[
1
]
],
[
[
1
],
[
1
],
[
1
]
],
[
... | https://geodesicpartners.co.uk/ml-gru-cell |
ml-beam-search | Beam search decoding | Hard | beam_search(start, trans, T, B) | import numpy as np
def beam_search(start, trans, T, B):
# Return [best_sequence, best_score].
pass | [
{
"args": [
[
-0.1,
-2.5
],
[
[
-2.5,
-0.1
],
[
-0.1,
-2.5
]
],
3,
1
],
"out": [
[
0,
1,
0
],
-0.30000000000000004
]
},
{
"arg... | https://geodesicpartners.co.uk/ml-beam-search |
ml-cosine-top-k | Top-k search by cosine similarity | Easy | cosine_top_k(q, M, k) | import numpy as np
def cosine_top_k(q, M, k):
# Return a list of k row indices, most similar first.
pass | [
{
"args": [
[
1,
0
],
[
[
1,
0
],
[
0,
1
],
[
1,
1
],
[
-1,
0
]
],
2
],
"out": [
0,
2
]
},
{
... | https://geodesicpartners.co.uk/ml-cosine-top-k |
ml-info-nce-loss | The InfoNCE contrastive loss | Medium | info_nce(Q, K, tau) | import numpy as np
def info_nce(Q, K, tau):
# Return the loss as a float.
pass | [
{
"args": [
[
[
1,
0
],
[
0,
1
]
],
[
[
1,
0
],
[
0,
1
]
],
1
],
"out": 0.3132616875
},
{
"args": [
[
[
... | https://geodesicpartners.co.uk/ml-info-nce-loss |
ml-negative-sampling | Skip-gram with negative sampling: loss and gradients | Hard | sgns_loss_grad(v, u, U_neg) | import numpy as np
def sgns_loss_grad(v, u, U_neg):
# Return [loss, grad_v, grad_u, grad_U_neg].
pass | [
{
"args": [
[
1,
0
],
[
1,
0
],
[
[
0,
1
]
]
],
"out": [
1.0064088681,
[
-0.2689414214,
0.5
],
[
-0.2689414214,
0
],
[
[
... | https://geodesicpartners.co.uk/ml-negative-sampling |
ml-k-nearest-neighbors | k-nearest neighbours classifier | Easy | knn_predict(X_train, y_train, X_test, k) | import numpy as np
def knn_predict(X_train, y_train, X_test, k):
# Return a list of predicted labels, one per row of X_test.
pass | [
{
"args": [
[
[
0,
0
],
[
1,
0
],
[
5,
5
],
[
6,
5
]
],
[
0,
0,
1,
1
],
[
[
0.5,
... | https://geodesicpartners.co.uk/ml-k-nearest-neighbors |
ml-k-means-clustering | k-means clustering (Lloyd's algorithm) | Medium | kmeans(X, init, max_iter) | import numpy as np
def kmeans(X, init, max_iter):
# Return [centroids (k x d), labels (n)].
pass | [
{
"args": [
[
[
0,
0
],
[
0,
1
],
[
10,
10
],
[
10,
11
]
],
[
[
0,
0
],
[
10,
10
... | https://geodesicpartners.co.uk/ml-k-means-clustering |
ml-pca | Principal component analysis | Medium | pca(X, k) | import numpy as np
def pca(X, k):
# Return [components (k x d), projected (n x k)].
pass | [
{
"args": [
[
[
1,
1
],
[
2,
2
],
[
3,
3
]
],
1
],
"out": [
[
[
0.7071067812,
0.7071067812
]
],
[
[
-1.414... | https://geodesicpartners.co.uk/ml-pca |
ml-decision-tree-split | Best decision-tree split by Gini impurity | Medium | best_split(X, y) | import numpy as np
def best_split(X, y):
# Return [feature, threshold, weighted_gini].
pass | [
{
"args": [
[
[
1
],
[
2
],
[
3
],
[
4
]
],
[
0,
0,
1,
1
]
],
"out": [
0,
2.5,
0
]
},
{
"args": [
[
... | https://geodesicpartners.co.uk/ml-decision-tree-split |
ml-gaussian-naive-bayes | Gaussian naive Bayes classifier | Medium | gaussian_nb(X_train, y_train, X_test) | import numpy as np
def gaussian_nb(X_train, y_train, X_test):
# Return the predicted label for each row of X_test, as a list.
pass | [
{
"args": [
[
[
0,
0
],
[
1,
1
],
[
0,
1
],
[
5,
5
],
[
6,
6
],
[
5,
6
]
],
[
... | https://geodesicpartners.co.uk/ml-gaussian-naive-bayes |
ml-gmm-em-step | One EM step for a Gaussian mixture | Medium | em_step(x, pi, mu, var) | import numpy as np
def em_step(x, pi, mu, var):
# Return [new_pi, new_mu, new_var, loglik].
pass | [
{
"args": [
[
-1,
1
],
[
0.5,
0.5
],
[
0,
0
],
[
1,
1
]
],
"out": [
[
0.5,
0.5
],
[
0,
0
],
[
1,
1
],
... | https://geodesicpartners.co.uk/ml-gmm-em-step |
ml-viterbi-algorithm | The Viterbi algorithm for a hidden Markov model | Medium | viterbi(start, trans, emit, obs) | import numpy as np
def viterbi(start, trans, emit, obs):
# Return [path (list of states), logp (float)].
pass | [
{
"args": [
[
0.6000000000000001,
0.4
],
[
[
0.7000000000000001,
0.30000000000000004
],
[
0.4,
0.6000000000000001
]
],
[
[
0.5,
0.4,
0.1
],
... | https://geodesicpartners.co.uk/ml-viterbi-algorithm |
ml-markov-stationary-distribution | Stationary distribution of a Markov chain | Easy | stationary(P) | import numpy as np
def stationary(P):
# Return the stationary distribution as a list.
pass | [
{
"args": [
[
[
0.9,
0.1
],
[
0.5,
0.5
]
]
],
"out": [
0.8333333333,
0.1666666667
]
},
{
"args": [
[
[
0,
1
],
[
0.5,
0.5
... | https://geodesicpartners.co.uk/ml-markov-stationary-distribution |
ml-running-variance | Running mean and variance in one pass | Easy | running_stats(xs) | def running_stats(xs):
# Return [[mean, variance], ...], one record after each value.
pass | [
{
"args": [
[
2,
4,
6
]
],
"out": [
[
2,
0
],
[
3,
2
],
[
4,
4
]
]
},
{
"args": [
[
1000000004,
1000000007,
1000000013,
1000000016
... | https://geodesicpartners.co.uk/ml-running-variance |
ml-roc-auc | ROC AUC from scores, with ties | Medium | roc_auc(scores, labels) | import numpy as np
def roc_auc(scores, labels):
# Return the AUC as a float.
pass | [
{
"args": [
[
0.9,
0.8,
0.30000000000000004,
0.1
],
[
1,
1,
0,
0
]
],
"out": 1
},
{
"args": [
[
0.5,
0.5,
0.5,
0.5
],
[
1,
0,
1,
... | https://geodesicpartners.co.uk/ml-roc-auc |
ml-spearman-rank-correlation | Spearman rank correlation (the information coefficient) | Medium | spearman(x, y) | import numpy as np
def spearman(x, y):
# Return the Spearman rank correlation as a float.
pass | [
{
"args": [
[
1,
2,
3,
4
],
[
10,
20,
30,
40
]
],
"out": 1
},
{
"args": [
[
1,
2,
3,
4
],
[
1,
8,
27,
1000
]
],
... | https://geodesicpartners.co.uk/ml-spearman-rank-correlation |
ml-autocorrelation-function | The autocorrelation function of a series | Easy | autocorrelation(x, max_lag) | import numpy as np
def autocorrelation(x, max_lag):
# Return [r_0, r_1, ..., r_max_lag].
pass | [
{
"args": [
[
1,
2,
3,
4,
5
],
2
],
"out": [
1,
0.4,
-0.1
]
},
{
"args": [
[
1,
-1,
1,
-1,
1,
-1
],
1
],
"out": [
1,
-0.8333333333... | https://geodesicpartners.co.uk/ml-autocorrelation-function |
ml-ols-standard-errors | Regression coefficients with standard errors and t-statistics | Medium | ols_inference(X, y) | import numpy as np
def ols_inference(X, y):
# Return [beta, se, t], each a list of p floats.
pass | [
{
"args": [
[
[
1,
0
],
[
1,
1
],
[
1,
2
],
[
1,
3
]
],
[
1,
3,
2,
5
]
],
"out": [
[
1.1,
... | https://geodesicpartners.co.uk/ml-ols-standard-errors |
ml-permutation-test | An exact permutation test for a difference in means | Medium | permutation_p_value(a, b) | from itertools import combinations
def permutation_p_value(a, b):
# Return the exact two-sided p-value as a float.
pass | [
{
"args": [
[
7,
9,
12
],
[
3,
4,
6
]
],
"out": 0.1
},
{
"args": [
[
1,
2
],
[
1,
2
]
],
"out": 1
},
{
"args": [
[
5
],
[
... | https://geodesicpartners.co.uk/ml-permutation-test |
ml-kalman-filter-1d | A one-dimensional Kalman filter | Medium | kalman_filter(ys, q, r, m0, p0) | def kalman_filter(ys, q, r, m0, p0):
# Return [[mean, variance], ...], one record after each observation.
pass | [
{
"args": [
[
10,
12,
11
],
1,
4,
8,
9
],
"out": [
[
9.3846153846,
2.7692307692
],
[
10.653465346499999,
1.9405940594
],
[
10.8002853067,
1.694721826
]
]
... | https://geodesicpartners.co.uk/ml-kalman-filter-1d |
ml-ndcg-at-k | NDCG at k | Easy | ndcg_at_k(rels, k) | import numpy as np
def ndcg_at_k(rels, k):
# Return NDCG@k as a float.
pass | [
{
"args": [
[
3,
2,
3,
0,
1,
2
],
6
],
"out": 0.9488107486
},
{
"args": [
[
0,
0,
0
],
3
],
"out": 0
},
{
"args": [
[
1,
0,
0
],
1... | https://geodesicpartners.co.uk/ml-ndcg-at-k |
ml-expected-calibration-error | Expected calibration error | Medium | expected_calibration_error(p, y, m) | import numpy as np
def expected_calibration_error(p, y, m):
# Return ECE as a float.
pass | [
{
"args": [
[
0.1,
0.2,
0.8,
0.9
],
[
0,
0,
1,
1
],
2
],
"out": 0.15
},
{
"args": [
[
1,
1,
0
],
[
1,
1,
0
],
10
],
... | https://geodesicpartners.co.uk/ml-expected-calibration-error |
ml-macro-f1 | Macro-averaged F1 across classes | Easy | macro_f1(y_true, y_pred) | import numpy as np
def macro_f1(y_true, y_pred):
# Return macro-F1 as a float.
pass | [
{
"args": [
[
0,
0,
1,
1,
2
],
[
0,
1,
1,
1,
0
]
],
"out": 0.4333333333
},
{
"args": [
[
5,
5,
5
],
[
5,
5,
5
]
],
... | https://geodesicpartners.co.uk/ml-macro-f1 |
ML coding interview problems
40 problems of the kind set in the implementation round of ML and quant interviews: softmax that doesn't overflow, a backward pass, attention, AUC with ties. Each row has a Python starter and a test table, so it also works as a small code-generation benchmark. Every problem's page: https://geodesicpartners.co.uk/machine-learning-coding
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