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"01a0d242-7caf-734a-bdd1-bb7381bce09c", "title": "Truncated SVD as the best matrix approximation in Frobenius norm", "url": "https://statisticaloddsandends.wordpress.com/2023/04/29/truncated-svd-as-the-best-matrix-approximation-in-frobenius-norm/", "published_at": "2023-04-29T07:33:28+00:00" }, { "id": "01a0d242-7caf-734a-bdd1-bb73826a4dfd", "title": "The Woodbury matrix identity and some special cases", "url": "https://statisticaloddsandends.wordpress.com/2023/04/18/the-woodbury-matrix-identity-and-some-special-cases/", "published_at": "2023-04-18T04:09:37+00:00" }, { "id": "01a0d242-7caf-734a-bdd1-bb738295276d", "title": "PHDG for solving the saddle point formulation of linear programs (LPs)", "url": "https://statisticaloddsandends.wordpress.com/2023/03/07/phdg-for-solving-the-saddle-point-formulation-of-linear-programs-lps/", "published_at": "2023-03-07T04:54:57+00:00" }, { "id": "01a0d242-7caf-734a-bdd1-bb7382e8314c", "title": "Proximal operator for inner product in R^n", "url": "https://statisticaloddsandends.wordpress.com/2023/03/03/proximal-operator-for-inner-product-in-rn/", "published_at": "2023-03-03T07:24:45+00:00" }, { "id": "01a0d242-7caf-734a-bdd1-bb738338c801", "title": "Strong duality for linear programs (LPs)", "url": "https://statisticaloddsandends.wordpress.com/2023/02/25/strong-duality-for-linear-programs-lps/", "published_at": "2023-02-25T15:57:26+00:00" }, { "id": "01a0d242-7caf-734a-bdd1-bb73833df222", "title": "Saddle point theorem for convex optimization", "url": "https://statisticaloddsandends.wordpress.com/2023/02/25/saddle-point-theorem-for-convex-optimization/", "published_at": "2023-02-25T15:47:25+00:00" }, { "id": "01a0d242-7caf-734a-bdd1-bb7383904e31", "title": "Deriving the dual of a linear program (LP)", "url": "https://statisticaloddsandends.wordpress.com/2023/02/25/deriving-the-dual-of-a-linear-program-lp/", "published_at": "2023-02-25T05:44:22+00:00" }, { "id": "01a0d242-7caf-734a-bdd1-bb7384415893", "title": "What is Moreau’s Decomposition Theorem?", "url": "https://statisticaloddsandends.wordpress.com/2023/02/04/what-is-moreaus-decomposition-theorem/", "published_at": "2023-02-04T20:44:47+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdeac55d23", "title": "Relations, resolvents and the proximal operator", "url": "https://statisticaloddsandends.wordpress.com/2023/02/04/relations-resolvents-and-the-proximal-operator/", "published_at": "2023-02-04T20:44:17+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdeafb6304", "title": "Convex conjugate functions, Fenchel’s inequality, subdifferentials and optimality", "url": "https://statisticaloddsandends.wordpress.com/2023/02/04/convex-conjugate-functions-fenchels-inequality-subdifferentials-and-optimality/", "published_at": "2023-02-04T05:00:20+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdeb636f59", "title": "What is Minkowski’s Representation Theorem?", "url": "https://statisticaloddsandends.wordpress.com/2022/12/30/what-is-minkowskis-representation-theorem/", "published_at": "2022-12-30T14:22:54+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdeba744bf", "title": "What is Sharpness-Aware Minimization (SAM)?", "url": "https://statisticaloddsandends.wordpress.com/2022/12/17/what-is-sharpness-aware-minimization-sam/", "published_at": "2022-12-17T16:59:06+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdec159780", "title": "O(n log n) algorithm for Euclidean projection onto a simplex", "url": "https://statisticaloddsandends.wordpress.com/2022/12/16/on-log-n-algorithm-for-euclidean-projection-onto-a-simplex/", "published_at": "2022-12-16T05:34:27+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdecfb035d", "title": "Optimality condition for Euclidean projection onto a convex polytope", "url": "https://statisticaloddsandends.wordpress.com/2022/12/10/optimality-condition-for-euclidean-projection-onto-a-convex-polytope/", "published_at": "2022-12-10T16:58:25+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cded17cb0b", "title": "Quasi-Newton methods: L-BFGS", "url": "https://statisticaloddsandends.wordpress.com/2022/11/26/quasi-newton-methods-l-bfgs/", "published_at": "2022-11-26T21:21:42+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdedbaeebe", "title": "Quasi-Newton methods: DFP and BFGS", "url": "https://statisticaloddsandends.wordpress.com/2022/11/26/quasi-newton-methods-dfp-and-bfgs/", "published_at": "2022-11-26T05:25:48+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdee0090b0", "title": "Quasi-Newton methods: SR1", "url": "https://statisticaloddsandends.wordpress.com/2022/11/24/quasi-newton-methods-sr1/", "published_at": "2022-11-24T21:59:16+00:00" }, { "id": "01a0d242-bdf8-70e1-885d-b6cdeece2cca", "title": "Quasi-Newton methods in optimization", "url": "https://statisticaloddsandends.wordpress.com/2022/11/24/quasi-newton-methods-in-optimization/", "published_at": "2022-11-24T03:42:27+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c03605dfbb", "title": "Exact line search and backtracking line search", "url": "https://statisticaloddsandends.wordpress.com/2022/11/19/exact-line-search-and-backtracking-line-search/", "published_at": "2022-11-19T06:11:37+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c036ca73b3", "title": "Affine hull vs. convex hull", "url": "https://statisticaloddsandends.wordpress.com/2022/11/18/affine-hull-vs-convex-hull/", "published_at": "2022-11-18T23:06:54+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c036e94ca1", "title": "What are the KKT conditions?", "url": "https://statisticaloddsandends.wordpress.com/2022/11/15/what-are-the-kkt-conditions/", "published_at": "2022-11-15T05:15:21+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c037772b39", "title": "Lagrange dual, weak duality and strong duality", "url": "https://statisticaloddsandends.wordpress.com/2022/11/12/lagrange-dual-weak-duality-and-strong-duality/", "published_at": "2022-11-12T17:23:59+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c0381d3d43", "title": "The Lagrange dual function is always concave", "url": "https://statisticaloddsandends.wordpress.com/2022/11/11/the-lagrange-dual-function-is-always-concave/", "published_at": "2022-11-11T17:30:09+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c03877780e", "title": "What is Danskin’s Theorem?", "url": "https://statisticaloddsandends.wordpress.com/2022/11/10/what-is-danskins-theorem/", "published_at": "2022-11-10T05:05:05+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c0391e9303", "title": "Asymptotic variance for a ratio of two estimators", "url": "https://statisticaloddsandends.wordpress.com/2022/10/14/asymptotic-variance-for-a-ratio-of-two-estimators/", "published_at": "2022-10-14T01:48:29+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c0391ec4b9", "title": "Understanding leaf node numbers when using rpart and rpart.rules", "url": "https://statisticaloddsandends.wordpress.com/2022/10/02/understanding-leaf-node-numbers-when-using-rpart-and-rpart-rules/", "published_at": "2022-10-02T23:04:52+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c039eec598", "title": "What is the exaggeration ratio (expected Type M error)?", "url": "https://statisticaloddsandends.wordpress.com/2022/09/27/what-is-the-exaggeration-ratio-expected-type-m-error/", "published_at": "2022-09-27T04:02:04+00:00" }, { "id": "01a0d242-f40d-7358-8585-35c03a4996e0", "title": "What is Type S error?", "url": "https://statisticaloddsandends.wordpress.com/2022/09/24/what-is-type-s-error/", "published_at": "2022-09-24T16:26:44+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575095c80f75", "title": "Lower bound of the correlation parameter for an equicorrelation matrix", "url": "https://statisticaloddsandends.wordpress.com/2022/09/23/lower-bound-of-the-correlation-parameter-for-an-equicorrelation-matrix/", "published_at": "2022-09-23T04:26:11+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575095d8b2c1", "title": "What is false positive risk?", "url": "https://statisticaloddsandends.wordpress.com/2022/09/07/what-is-false-positive-risk/", "published_at": "2022-09-07T03:55:29+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575096a9a76a", "title": "General chi-square tests", "url": "https://statisticaloddsandends.wordpress.com/2022/08/19/general-chi-square-tests/", "published_at": "2022-08-19T04:54:57+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575097a16872", "title": "Asymptotic distribution of the Pearson chi-square statistic", "url": "https://statisticaloddsandends.wordpress.com/2022/08/06/asymptotic-distribution-of-the-pearson-chi-square-statistic/", "published_at": "2022-08-06T05:52:52+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575098510544", "title": "Draft position for players in the NBA for the 2020-21 season", "url": "https://statisticaloddsandends.wordpress.com/2022/07/18/draft-position-for-players-in-the-nba-for-the-2020-21-season/", "published_at": "2022-07-18T04:53:06+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575098acda8e", "title": "Slight inconsistency between forcats’ fct_lump_min and fct_lump_prop", "url": "https://statisticaloddsandends.wordpress.com/2022/07/03/slight-inconsistency-between-forcats-fct_lump_min-and-fct_lump_prop/", "published_at": "2022-07-03T04:17:03+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575099446749", "title": "What is the synthetic control estimator?", "url": "https://statisticaloddsandends.wordpress.com/2022/06/28/what-is-the-synthetic-control-estimator/", "published_at": "2022-06-28T04:12:55+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575099afa95a", "title": "A quirk when using data.table?", "url": "https://statisticaloddsandends.wordpress.com/2022/06/04/a-quirk-when-using-data-table/", "published_at": "2022-06-04T04:57:52+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-575099ea530c", "title": "7 guiding principles for using synthetic control estimators", "url": "https://statisticaloddsandends.wordpress.com/2022/05/31/7-guiding-principles-for-using-synthetic-control-estimators/", "published_at": "2022-05-31T12:56:58+00:00" }, { "id": "01a0d243-1b7e-71e0-abc3-57509a6c7480", "title": "T-learners, S-learners and X-learners", "url": "https://statisticaloddsandends.wordpress.com/2022/05/20/t-learners-s-learners-and-x-learners/", "published_at": "2022-05-20T19:16:45+00:00" } ] posts Claim your blog

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2026

A few approximations for the standard normal distribution original ↗

20 Sept 2026

Pólya approximation for the standard normal distribution original ↗

19 Sept 2026

What is the Lincoln index?original ↗

5 Sept 2026

Brainteaser about the probability of two particular lines intersecting original ↗

19 Apr 2026

Brainteaser about max probability of a random variable being 0 given some constraints original ↗

1 Apr 2026

2025

What is a probability-generating function (PGF)?original ↗

10 Nov 2025

Brainteaser about points belonging to the same semicircular arc original ↗

31 Aug 2025

Brainteaser about expected number of rolls original ↗

30 Aug 2025

Downloading datasets from Our World in Data in R original ↗

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 distribution original ↗

7 Sept 2024

Converting a uniform distribution into a Cauchy distribution original ↗

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 stream original ↗

18 May 2024

Vectorization and Kronecker products original ↗

17 May 2024

The mixed-product property of the Kronecker product original ↗

17 May 2024

Rough approximations to move between logit and probability scales original ↗

8 May 2024

What is the Plackett-Luce model?original ↗

24 Apr 2024

CVaR and a lemma from Rockafellar & Uryasev original ↗

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 loss original ↗

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 outputs original ↗

23 Mar 2024

Conditional distributions for the linear Gaussian model original ↗

23 Mar 2024

Using the Laplace approximation to approximate a probability distribution original ↗

23 Mar 2024

What is a generalized second-price auction?original ↗

22 Mar 2024

Plots comparing momentum-based GD and Nesterov’s AGD original ↗

19 Mar 2024

The difference between momentum-based gradient descent and Nesterov’s accelerated gradient descent original ↗

15 Mar 2024

Basic ideas in reinforcement learning original ↗

28 Feb 2024

Stratified sampling in Scala/Spark with sampleBy()original ↗

24 Feb 2024

Some helpful functions in scala original ↗

11 Feb 2024

What is the Net Promoter Score (NPS)?original ↗

20 Jan 2024

2023

Column subset selection is equivalent to finding principal variables original ↗

27 Dec 2023

Projecting a random vector in R^q onto (the span of) a random vector R^p original ↗

26 Dec 2023

QuantEase: An optimization-based method for quantizing your model original ↗

21 Dec 2023

Example demonstrating why subgradient descent is not a descent method original ↗

21 Nov 2023

The pointwise maximum of (strongly) convex functions is (strongly) convex original ↗

19 Nov 2023

KL divergence between two normal distributions original ↗

16 Nov 2023

Conditional distribution for the multivariate normal distribution original ↗

14 Nov 2023

What is the swish activation function?original ↗

25 Oct 2023

Perplexity as an evaluation metric for ML models original ↗

24 Oct 2023

Cross-entropy and Gibbs’ inequality original ↗

17 Oct 2023

CDF of the log-normal distribution original ↗

10 Oct 2023

Normal distribution and uniform distribution symmetric around 0 do not have finite inverse first moments original ↗

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 two original ↗

30 Sept 2023

Danskin’s theorem as applied to the dual function original ↗

30 Sept 2023

A simple relationship between the PDF of the normal distribution and its derivative original ↗

22 Sept 2023

The relationship between the CDFs and PDFs of X and a monotonic transformation of X original ↗

9 Sept 2023

The relationship between the CDFs and PDFs of X and aX+b original ↗

8 Sept 2023

Optimality condition for Euclidean projection onto a convex polytope: A proof original ↗

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 function original ↗

11 Aug 2023

Python idioms for reading/writing from files/pickles original ↗

21 Jun 2023

More details on sharpness-aware minimization (SAM)original ↗

30 May 2023

Solving the dual norm problem original ↗

30 May 2023

Getting matplotlib’s default colors original ↗

24 May 2023

Truncated SVD as the best matrix approximation in Frobenius norm original ↗

29 Apr 2023

The Woodbury matrix identity and some special cases original ↗

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^n original ↗

3 Mar 2023

Strong duality for linear programs (LPs)original ↗

25 Feb 2023

Saddle point theorem for convex optimization original ↗

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 operator original ↗

4 Feb 2023

Convex conjugate functions, Fenchel’s inequality, subdifferentials and optimality original ↗

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 simplex original ↗

16 Dec 2022

Optimality condition for Euclidean projection onto a convex polytope original ↗

10 Dec 2022

Quasi-Newton methods: L-BFGS original ↗

26 Nov 2022

Quasi-Newton methods: DFP and BFGS original ↗

26 Nov 2022

Quasi-Newton methods: SR1 original ↗

24 Nov 2022

Quasi-Newton methods in optimization original ↗

24 Nov 2022

Exact line search and backtracking line search original ↗

19 Nov 2022

Affine hull vs. convex hull original ↗

18 Nov 2022

What are the KKT conditions?original ↗

15 Nov 2022

Lagrange dual, weak duality and strong duality original ↗

12 Nov 2022

The Lagrange dual function is always concave original ↗

11 Nov 2022

What is Danskin’s Theorem?original ↗

10 Nov 2022

Asymptotic variance for a ratio of two estimators original ↗

14 Oct 2022

Understanding leaf node numbers when using rpart and rpart.rules original ↗

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 matrix original ↗

23 Sept 2022

What is false positive risk?original ↗

7 Sept 2022

General chi-square tests original ↗

19 Aug 2022

Asymptotic distribution of the Pearson chi-square statistic original ↗

6 Aug 2022

Draft position for players in the NBA for the 2020-21 season original ↗

18 Jul 2022

Slight inconsistency between forcats’ fct_lump_min and fct_lump_prop original ↗

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 estimators original ↗

31 May 2022

T-learners, S-learners and X-learners original ↗

20 May 2022