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2026

A few approximations for the standard normal distributionoriginal ↗
20 Sept 2026
Pólya approximation for the standard normal distributionoriginal ↗
19 Sept 2026
What is the Lincoln index?original ↗
5 Sept 2026
Brainteaser about the probability of two particular lines intersectingoriginal ↗
19 Apr 2026
Brainteaser about max probability of a random variable being 0 given some constraintsoriginal ↗
1 Apr 2026

2025

What is a probability-generating function (PGF)?original ↗
10 Nov 2025
Brainteaser about points belonging to the same semicircular arcoriginal ↗
31 Aug 2025
Brainteaser about expected number of rollsoriginal ↗
30 Aug 2025
Downloading datasets from Our World in Data in Roriginal ↗
30 Jan 2025
What is the fused lasso?original ↗
17 Jan 2025

2024

What is the Cauchy combination test?original ↗
7 Sept 2024
An interesting result involving the Cauchy distributionoriginal ↗
7 Sept 2024
Converting a uniform distribution into a Cauchy distributionoriginal ↗
29 Aug 2024
What is Adam and AdamW?original ↗
27 Jun 2024
What is elastic weight consolidation?original ↗
26 Jun 2024
A simple probabilistic algorithm for estimating the number of distinct elements in a data streamoriginal ↗
18 May 2024
Vectorization and Kronecker productsoriginal ↗
17 May 2024
The mixed-product property of the Kronecker productoriginal ↗
17 May 2024
Rough approximations to move between logit and probability scalesoriginal ↗
8 May 2024
What is the Plackett-Luce model?original ↗
24 Apr 2024
CVaR and a lemma from Rockafellar & Uryasevoriginal ↗
15 Apr 2024
What is Conditional Value at Risk (CVaR)?original ↗
14 Apr 2024
What is Value at Risk (VaR)?original ↗
13 Apr 2024
What is focal loss?original ↗
12 Apr 2024
Softmax loss and sampled softmax lossoriginal ↗
4 Apr 2024
What is local SGD?original ↗
29 Mar 2024
What is Neural Thompson Sampling (NeuralTS)?original ↗
27 Mar 2024
Using the Laplace method to approximate the posterior distribution of neural network parameters and outputsoriginal ↗
23 Mar 2024
Conditional distributions for the linear Gaussian modeloriginal ↗
23 Mar 2024
Using the Laplace approximation to approximate a probability distributionoriginal ↗
23 Mar 2024
What is a generalized second-price auction?original ↗
22 Mar 2024
Plots comparing momentum-based GD and Nesterov’s AGDoriginal ↗
19 Mar 2024
The difference between momentum-based gradient descent and Nesterov’s accelerated gradient descentoriginal ↗
15 Mar 2024
Basic ideas in reinforcement learningoriginal ↗
28 Feb 2024
Stratified sampling in Scala/Spark with sampleBy()original ↗
24 Feb 2024
Some helpful functions in scalaoriginal ↗
11 Feb 2024
What is the Net Promoter Score (NPS)?original ↗
20 Jan 2024

2023

Column subset selection is equivalent to finding principal variablesoriginal ↗
27 Dec 2023
Projecting a random vector in R^q onto (the span of) a random vector R^poriginal ↗
26 Dec 2023
QuantEase: An optimization-based method for quantizing your modeloriginal ↗
21 Dec 2023
Example demonstrating why subgradient descent is not a descent methodoriginal ↗
21 Nov 2023
The pointwise maximum of (strongly) convex functions is (strongly) convexoriginal ↗
19 Nov 2023
KL divergence between two normal distributionsoriginal ↗
16 Nov 2023
Conditional distribution for the multivariate normal distributionoriginal ↗
14 Nov 2023
What is the swish activation function?original ↗
25 Oct 2023
Perplexity as an evaluation metric for ML modelsoriginal ↗
24 Oct 2023
Cross-entropy and Gibbs’ inequalityoriginal ↗
17 Oct 2023
CDF of the log-normal distributionoriginal ↗
10 Oct 2023
Normal distribution and uniform distribution symmetric around 0 do not have finite inverse first momentsoriginal ↗
9 Oct 2023
Finite-difference stochastic approximation (FDSA) and simultaneous perturbation stochastic approximation (SPSA)original ↗
3 Oct 2023
Harmonic mean of two numbers is (much) closer to the smaller of the twooriginal ↗
30 Sept 2023
Danskin’s theorem as applied to the dual functionoriginal ↗
30 Sept 2023
A simple relationship between the PDF of the normal distribution and its derivativeoriginal ↗
22 Sept 2023
The relationship between the CDFs and PDFs of X and a monotonic transformation of Xoriginal ↗
9 Sept 2023
The relationship between the CDFs and PDFs of X and aX+boriginal ↗
8 Sept 2023
Optimality condition for Euclidean projection onto a convex polytope: A prooforiginal ↗
22 Aug 2023
What’s the probability of getting all heads for coin flips (assuming we get to retry k times)?original ↗
19 Aug 2023
The softplus functionoriginal ↗
11 Aug 2023
Python idioms for reading/writing from files/picklesoriginal ↗
21 Jun 2023
More details on sharpness-aware minimization (SAM)original ↗
30 May 2023
Solving the dual norm problemoriginal ↗
30 May 2023
Getting matplotlib’s default colorsoriginal ↗
24 May 2023
Truncated SVD as the best matrix approximation in Frobenius normoriginal ↗
29 Apr 2023
The Woodbury matrix identity and some special casesoriginal ↗
18 Apr 2023
PHDG for solving the saddle point formulation of linear programs (LPs)original ↗
7 Mar 2023
Proximal operator for inner product in R^noriginal ↗
3 Mar 2023
Strong duality for linear programs (LPs)original ↗
25 Feb 2023
Saddle point theorem for convex optimizationoriginal ↗
25 Feb 2023
Deriving the dual of a linear program (LP)original ↗
25 Feb 2023
What is Moreau’s Decomposition Theorem?original ↗
4 Feb 2023
Relations, resolvents and the proximal operatororiginal ↗
4 Feb 2023
Convex conjugate functions, Fenchel’s inequality, subdifferentials and optimalityoriginal ↗
4 Feb 2023

2022

What is Minkowski’s Representation Theorem?original ↗
30 Dec 2022
What is Sharpness-Aware Minimization (SAM)?original ↗
17 Dec 2022
O(n log n) algorithm for Euclidean projection onto a simplexoriginal ↗
16 Dec 2022
Optimality condition for Euclidean projection onto a convex polytopeoriginal ↗
10 Dec 2022
Quasi-Newton methods: L-BFGSoriginal ↗
26 Nov 2022
Quasi-Newton methods: DFP and BFGSoriginal ↗
26 Nov 2022
Quasi-Newton methods: SR1original ↗
24 Nov 2022
Quasi-Newton methods in optimizationoriginal ↗
24 Nov 2022
Exact line search and backtracking line searchoriginal ↗
19 Nov 2022
Affine hull vs. convex hulloriginal ↗
18 Nov 2022
What are the KKT conditions?original ↗
15 Nov 2022
Lagrange dual, weak duality and strong dualityoriginal ↗
12 Nov 2022
The Lagrange dual function is always concaveoriginal ↗
11 Nov 2022
What is Danskin’s Theorem?original ↗
10 Nov 2022
Asymptotic variance for a ratio of two estimatorsoriginal ↗
14 Oct 2022
Understanding leaf node numbers when using rpart and rpart.rulesoriginal ↗
2 Oct 2022
What is the exaggeration ratio (expected Type M error)?original ↗
27 Sept 2022
What is Type S error?original ↗
24 Sept 2022
Lower bound of the correlation parameter for an equicorrelation matrixoriginal ↗
23 Sept 2022
What is false positive risk?original ↗
7 Sept 2022
General chi-square testsoriginal ↗
19 Aug 2022
Asymptotic distribution of the Pearson chi-square statisticoriginal ↗
6 Aug 2022
Draft position for players in the NBA for the 2020-21 seasonoriginal ↗
18 Jul 2022
Slight inconsistency between forcats’ fct_lump_min and fct_lump_proporiginal ↗
3 Jul 2022
What is the synthetic control estimator?original ↗
28 Jun 2022
A quirk when using data.table?original ↗
4 Jun 2022
7 guiding principles for using synthetic control estimatorsoriginal ↗
31 May 2022
T-learners, S-learners and X-learnersoriginal ↗
20 May 2022
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