Articles, newest first
Spectral Clustering: The Graph Is the Model
Spectral clustering converts a similarity graph into an eigenvector embedding and then clusters that embedding. The graph construction is the model.
Read article
Clustering Is a Model of Similarity
Clustering does not discover a unique hidden partition of data. It produces groups relative to a representation, similarity measure, algorithm, and scale.
Read article
Topological Data Analysis: Shape Across Scales
Topological data analysis summarizes multiscale shape through constructions such as persistent homology and Mapper, but topology does not make high-dimension...
Read article
Customer Lifetime Value: Expected Future Contribution
Customer lifetime value is an expected discounted future contribution under assumptions about activity, retention, margin, censoring, and intervention.
Read article
Monte Carlo Methods: Sampling, Error, and Variance Reduction
Monte Carlo methods approximate expectations with random samples. MCMC is one important special case, not a synonym for Monte Carlo.
Read article
Probabilistic Programming and MCMC
Probabilistic programming separates model specification from inference, but inference still depends on diagnostics, geometry, and numerical stability.
Read article
The Normal Distribution: Why the Bell Curve Appears
The normal distribution is important because of Gaussian models, additive noise, asymptotic approximations, and the central limit theorem—not because real da...
Read articleMarina Viazovska and the E8 Sphere-Packing Proof
Marina Viazovska solved the eight-dimensional sphere-packing problem by constructing the exact auxiliary function needed to prove optimality of the E8 lattice.
Read article
Text Preprocessing in NLP: When Cleaning Helps and Hurts
Text preprocessing is model-dependent. Lowercasing, stemming, stop-word removal, normalization, and tokenization can help some pipelines and damage others.
Read article
Mathematics of Machine Learning: Risk and Generalization
The mathematics of machine learning is a study of risk, approximation, optimization, and generalization under finite data.
Read article