Computational statistics
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-2962 Exact uniform sampling of arbitrary-margin contingency tables
- Math-2964 FPRAS for cell-bounded contingency tables
- Math-2975 Memory–precision lower bounds for exact Gaussian regression
- Math-3790 10 Lectures and 42 Open Problems — Tightness of the Multireference Alignment SDP
- Math-4378 10 Lectures and 42 Open Problems — Consistency and sample complexity of Multireference Alignment
- Math-4381 Linear collapse, binomial hypersurfaces, and the image of local-odds fibers
- Math-4382 Compatible and complete odds-ratio specifications
- Math-4384 Unique minimal Markov bases, bipartite cycles, and padding monotonicity
- Math-4385 An algebraic one-mode certificate for MANOVA
- Math-4386 Exact slack lifts for Markov bases under rounded summaries
- Math-4387 Binary independence and hierarchical models in cumulant coordinates
- Math-4388 Holonomic Bayesian normalizers with certified posterior moments
- Math-4389 Transcendence-aware algebraic localization of symmetric Gaussian-mixture modes
- Math-4392 Gaussian observed-likelihood equations and a rank-certified monotone solution
- Math-4393 Finite Markov templates with several varying level sets
- Math-4394 Quartic Markov bases and saturated simplicial leaves
- Math-4396 Fourier edge invariants and a visibility threshold for finite rate-class mixtures
- Math-4401 ML degree, feasibility, and a Gaussian likelihood-root trichotomy
- Math-4403 Exact Bayesian evidence and prediction for finite latent discrete models
- Math-4404 Markov-basis complexity depends on representation
- Math-4405 Equality constraints do not characterize hidden-variable models
- Math-4408 Arbitrary logistic cell gaps with positive margins and ordinary-margin obstructions
- Math-4410 Explicit Gaussian MLE for monotone block missingness
- Math-4412 An exact MLE fiber for the smallest binary hidden-variable model
- Math-4413 Saturation-aware exceptional likelihood fibers and the 2x2 independence locus
- Math-4414 Covariance-whitened polynomial invariants for model goodness of fit
- Math-4416 Finite-field least squares as statistical decoding
- Math-4442 Spectral laws for Gaussian multiple-shift states
- Math-4502 Density and Geometry Recovery from Nearest-Neighbor Graphs
- Math-4503 Polynomial-Time Algorithms for High-Dimensional Private Queries
- Math-4522 Accurate Answers to Adaptively Chosen Statistical Queries
- Math-4536 Information–Computation Gaps in Sparse Linear Regression
- Math-4538 Extrapolating Clusterings from Semidefinite Subsamples
- Math-4591 Type-II Error Exponents in Distributed Hypothesis Testing
- Math-4594 Gaussian Mean Testing under Information Constraints
- Math-4609 Online Model Selection for Nonparametric Classes
- Math-4615 Semi-Supervised Sparse Gaussian Classification
- Math-4624 Efficient Verification of Distribution Properties
- Math-5001 A finite-sample Rao-Blackwell diagnostic between Kalman and particle filtering
- Math-5010 Degree-two-and-three Markov basis for the Birkhoff ranking model
- Math-5011 Indispensable cubics and a five-move Markov basis on the zero-middle-row face
- Math-5012 Two fixed odds ratios form a line segment, with a complete boundary audit
- Math-5013 A binary-collapse-invisible likelihood face
- Math-5015 Sufficient releases, conditional fibers, and incompatible Gibbs updates
- Math-5016 Exact cumulant ideal of the normalized binary four-cycle
- Math-5017 BIC evidence, mixture singularities, and an exact quotient diagnostic
- Math-5021 Behrens–Fisher likelihood equations and an equal-scatter bifurcation
- Math-5022 Semialgebraic stratification of maximum likelihood
- Math-5026 A joint tree and JC69/K80 selector with a finite-sample certificate
- Math-5028 An ancestral-observation certificate for likelihood unimodality