# functional_analysis

Bayesian inverse problems in function space
a.k.a. Bayesian calibration, model uncertainty for PDEs and other wibbly, blobby things
2020-10-13
– 2022-09-26Gaussian process inference by partial updates
2020-12-03
– 2022-09-22Conditional expectation and probability
2020-02-04
– 2022-09-21Posterior Gaussian process samples by updating prior samples
Matheron’s other weird trick
2020-12-03
– 2022-09-20Gaussian process regression
And classification. And extensions.
2019-12-03
– 2022-09-20Neural process regression
2019-12-03
– 2022-09-20Penalised/regularised regression
2016-06-23
– 2022-09-19Gradient descent, first-order, stochastic
a.k.a. SGD, as seen in deep learning
2020-01-30
– 2022-09-05Precision matrix estimation
Especially Gaussain
2014-11-16
– 2022-09-05Distributional robustness in inference
2019-07-12
– 2022-08-30Mellin transforms
2021-01-29
– 2022-08-28Automatic differentiation
2016-07-27
– 2022-08-09Automatic differentiation in Julia
2016-07-27
– 2022-08-09Scaling laws for very large neural nets
Compute/size/data tradeoffs
2021-01-14
– 2022-08-09Learning Gamelan
2016-04-05
– 2022-08-05Gaussian process regression software
And classification.
2019-12-03
– 2022-07-29Gradient descent, Newton-like
2019-02-05
– 2022-07-25Partial differential equations
2021-01-27
– 2022-07-23Fun tricks in non-convex optimisation
2014-10-04
– 2022-07-14Empirical mode decomposition
Multiplying your exposure to uncertainty principles
2018-01-06
– 2022-07-12Inverse problems
2016-03-30
– 2022-06-30Approximate matrix factorisation
Sometimes even exact
2014-08-05
– 2022-06-29Signal sampling
Discrete representation of continuous signals and converse
2017-05-30
– 2022-06-24Emergent spacetime
What are qubits again?
2022-05-26Graph neural nets
2020-09-16
– 2022-05-18Exponential families
2016-04-19
– 2022-05-13Numerical PDE solvers
2016-03-01
– 2022-05-02Generalized Bayesian Computation
2019-10-03
– 2022-04-28Gradient descent
First order of business
2014-10-04
– 2022-04-28Bayesian nonparametric statistics
Updating more dimensions than datapoints
2016-05-30
– 2022-04-07Orthonormal and unitary matrices
Energy preserving operators, generalized rotations
2019-10-22
– 2022-04-05Matrix calculus
2018-07-09
– 2022-04-04Measure-valued random variates
Including completely random measures and many generalizations
2020-10-16
– 2022-03-30Wiener-Khintchine representations
Spectral representations of stochastic processes
2019-05-08
– 2022-03-11Fun with rotational symmetries
2021-01-29
– 2022-03-03Stability in dynamical systems
Lyapunov exponents and ilk
2019-05-21
– 2022-02-22Optimal transport inference
I feel the earth mover under my feet, I feel the ψ tumbling down, I feel my heart start to trembling, Whenever you’re around my empirical density in minimal transport cost
2021-03-16
– 2022-02-22Neural nets for “implicit representations”
2021-01-21
– 2022-02-01Karhunen-Loève expansions
2019-09-16
– 2022-02-01Learning on manifolds
Finding the lowest bit of a krazy straw, from the inside
2011-10-21
– 2022-01-26(Outlier) robust statistics
2014-11-25
– 2022-01-21Bayesian inverse problems
2016-03-30
– 2022-01-13Time frequency analysis
Multiplying your exposure to uncertainty principles
2018-01-06
– 2021-12-21Gradient descent, Newton-like, stochastic
2020-01-23
– 2021-12-09Convolutional subordinator processes
2021-03-08
– 2021-12-01Random rotations
2021-05-18
– 2021-12-01Neural nets for “implicit representations”
2021-01-21
– 2021-11-16Optimisation
2014-10-04
– 2021-11-11High dimensional statistics
2015-03-12
– 2021-10-28Hyperparameter optimization
Replacing a hyperparameter problem with a hyperhyperparameter problem which feels like progress I guess
2020-09-25
– 2021-10-20Fun with determinants
Especially Jacobian determinants
2011-04-06
– 2021-10-12Multilinear algebra
Outer products, tensors, einstein summation
2021-10-08Polynomial bases
2021-01-29
– 2021-10-06Gradient descent at scale
Practical implementation of large optimisations
2021-07-14
– 2021-09-28Meta learning
Few-shot learning, learning fast weights, learning to learn
2021-09-16Fractional differential equations
2016-03-22
– 2021-09-13Wirtinger calculus
It’s not complicated / It’s complex
2019-05-08
– 2021-09-07Path smoothness properties of stochastic processes
Continuity, differentiability and other smoothness properties
2020-02-26
– 2021-09-02Sequential experiments
Especially multiple sequential experiments
2021-08-04Learning summary statistics
2020-04-22
– 2021-07-15Optimal transport metrics
Wasserstein distances, Monge-Kantorovich metrics, Earthmover distances
2019-05-30
– 2021-06-08Stein’s method
2021-03-12
– 2021-06-01Isotropic random vectors
2011-08-10
– 2021-05-24Randomized low dimensional projections
2021-03-12
– 2021-05-24Fourier transforms
2021-01-29
– 2021-04-26Differentiable model selection
Differentiable hyperparameter search, and architecture search, and optimisation optimisation by optimisation and so on
2020-09-25
– 2021-04-13Generically approximating probability distributions
2021-03-12
– 2021-03-22Matrix measure concentration inequalities and bounds
2014-11-25
– 2021-03-08Measure concentration inequalities
On being 80% sure I am only 20% wrong
2014-11-25
– 2021-03-04Frames and Riesz bases
Generalisations of orthogonal bases
2017-06-12
– 2021-02-24Causal inference in the continuous limit
2021-02-17Stability in linear dynamical systems
This Bodes well
2019-07-19
– 2021-02-16Integral transforms
2021-01-29
– 2021-01-30Random embeddings and hashing
2016-12-05
– 2020-12-01Randomised regression
2017-01-13
– 2020-12-01Distribution regression
2020-12-01Weighted data in statistics
2020-11-04
– 2020-11-06Automatic design of experiments
Minesweeper++
2017-04-11
– 2020-10-13Sparse model selection
2016-09-05
– 2020-10-02AutoML
2017-07-17
– 2020-10-02Data summarization
On maps drawn at smaller than 1:1 scale
2019-01-14
– 2020-09-18Independence, conditional, statistical
2016-04-21
– 2020-09-13Dimensionality reduction
Wherein I teach myself, amongst other things, feature selection, how a sparse PCA works, and decide where to file multidimensional scaling
2015-03-22
– 2020-09-11Learning of manifolds
Also topological data analysis; other hip names to follow
2014-08-19
– 2020-06-23Functional regression
2016-01-05
– 2020-05-28Natural gradient descent
Climbing slower on the tricky bits
2019-07-18
– 2020-05-26Restricted isometry properties
Plus incoherence, irrepresentability, and other uncertainty bounds for a sparse world, and maybe frame theory, what’s that now?
2017-06-12
– 2020-03-09Kernel approximation
2016-07-27
– 2020-03-06Random change of time
Stochastic processes derived by varying the rate of time’s passage, which is more convenient than I imagined
2015-08-05
– 2020-02-10Branching processes
2014-08-18
– 2020-02-07(Reproducing) kernel tricks
2014-08-18
– 2020-01-20Information geometry
2011-10-21
– 2019-12-27Hawkes processes
2019-12-22Convergence of random variables
2019-12-03Gradient descent, Higher order
2019-10-26Sparse regression
2016-06-23
– 2019-10-24Discrete time Fourier and related transforms
Also, chirplets, z-transforms, chromatic derivatives…
2019-10-17
– 2019-10-17Density estimation
Especially non- or semiparametrically
2016-06-06
– 2019-10-16Non-negative matrix factorisation
2019-10-14Zeros of random trigonometric polynomials
2019-05-20
– 2019-10-14Covariance matrix estimation
Esp Gaussian
2014-11-16
– 2019-09-21Representer theorems
2019-09-16Probability
2011-07-29
– 2019-07-15Semidefinite proramming
2019-06-29Fourier interpolation
2019-06-19Wiener theorem
Now with bonus Bochner!
2019-05-08Wacky regression
2015-09-23
– 2019-05-02Ordinary differential equations
Thou, silent form, dost tease us out of thought / As doth eternity
2019-03-28Inner product spaces
The most highly developed theory of squaring things
2019-01-01
– 2019-02-11Nearly sufficient statistics
How about “Sufficient sufficiency”? — is that taken?
2018-03-13
– 2019-01-14Decaying sinusoid dictionaries
2019-01-07Normed spaces
2019-01-01
– 2019-01-04Optimisation, combinatorial
2018-08-11Linear algebra
If the thing is twice as big, the transformed version of the thing is also twice as big. {End}
2011-04-06
– 2018-08-07Integral probability metrics
2016-08-21
– 2017-10-31Gradient descent, continuous, primal/dual formulations.
2017-08-07Warping and registration problems
Matching up of bumps and wibbles in stretchy things
2016-08-17
– 2017-07-23Lagrangian mechanics
2015-02-11
– 2017-06-18Compressed sensing and sampling
A fancy ways of counting zero
2014-08-18
– 2017-06-14Uncertainty principles
2017-05-14Functional equations
Putting the funk in functions
2017-02-06
– 2017-02-19Metric entropy
2017-02-13Differential geometry, geometric algebra etc
2014-11-27
– 2016-10-13Statistical learning theory
Eventually including structural risk minimisation, risk bounds, hopefully-uniform convergence rates, VC-dimension, generalisation-and-stability framings etc
2016-07-06
– 2016-08-16Randomised linear algebra
2016-08-16Blind deconvolution
2015-03-01
– 2016-07-27Matrix norms, divergences, metrics
2016-06-03
– 2016-06-15Function approximation and interpolation
2016-06-09Iterated function systems
2014-08-14
– 2016-06-06Deconvolution
2015-04-19
– 2016-04-11Sigma algebras, probability spaces, measure theory
The scaffolding of randomness
2015-06-20