## Trade-offs in Statistical Learning      4 views

 Title Trade-offs in Statistical Learning Title of Series Computational and statistical trade-offs in learning Part Number 8 Number of Parts 10 Author Berthet, Quentin License CC Attribution 3.0 Unported:You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. Identifiers 10.5446/20251 (DOI) Publisher Institut des Hautes Études Scientifiques (IHÉS) Release Date 2016 Language English

 Subject Area Mathematics Abstract I will explore the notion of constraints on learning procedures, and discuss the impact that they can have on statistical precision. This is inspired by real-life concerns such as limits on time for computation, on reliability of observations, or communication between agents. I will show how these constraints can be shown to have a concrete cost on the statistical performance of these procedures, by describing several examples. Complex (psychology) State of matter Multiplication sign Decision theory 1 (number) Parameter (computer programming) Subset Summation Mathematics Statistics Higgs mechanism Injektivität Linear regression Gradient Interior (topology) Functional (mathematics) Hypothesis Sparse matrix Order (biology) Right angle Figurate number Mathematical optimization Combinatorics Point (geometry) Standard error Statistics Algebraic structure Barrelled space Average Number Hypothesis Average Mathematical optimization Units of measurement Condition number Statistical hypothesis testing Sine Algebraic structure Set (mathematics) Line (geometry) Estimator Voting Event horizon Computer animation Estimation Object (grammar) Mathematical optimization Family Statistical hypothesis testing
Euclidean vector Randomization Distribution (mathematics) Multiplication sign Direction (geometry) 1 (number) Bound state Independence (probability theory) Summation Order (biology) Vector space Square number Statistics Position operator Area Constraint (mathematics) Infinity Perturbation theory Statistical hypothesis testing Hypothesis Distance Maxima and minima Arithmetic mean Sparse matrix Vector space Hausdorff dimension Order (biology) Right angle Resultant Point (geometry) Standard error Slide rule Statistics Divisor Distribution (mathematics) Random matrix Mathematical analysis Sparse matrix Distance Rule of inference Glattheit <Mathematik> Subtraction Curve fitting Standard deviation Principal ideal Vector graphics Mathematical analysis Bound state Independence (probability theory) Covariance matrix Quadratic form Power (physics) Computer animation Principal component analysis Dependent and independent variables Units of measurement Mathematical optimization Statistical hypothesis testing
Statistical hypothesis testing Statistics Polynomial Logarithm Multiplication sign Bound state Mathematical analysis Theory Infinity Bound state Mortality rate Statistical hypothesis testing Computer animation Order (biology) Heuristic Energy level Diagonal Analytic continuation Statistical hypothesis testing
Randomization Clique problem Distribution (mathematics) Graph (mathematics) Multiplication sign Parameter (computer programming) Variance Subset Expected value Summation Matrix (mathematics) Lattice (order) Square number Moving average Noise Arc (geometry) Position operator Logical constant Polynomial Link (knot theory) Hypothesis Random graph Maxima and minima Angle Chain Right angle Energy level Resultant Reduction of order Thomas Bayes Point (geometry) Spectrum (functional analysis) Random number Statistics Vapor barrier Link (knot theory) Connectivity (graph theory) Distribution (mathematics) Average Sparse matrix Theory Number Reduction of order Adjacency matrix Algebraic structure Expected value Maxwell's demon Computer animation Vertex (graph theory) Graph (mathematics) Units of measurement Mathematical optimization
Logical constant Complex (psychology) Group action Clique problem Resonator Water vapor Perspective (visual) Explosion Summation Sign (mathematics) Insertion loss Convex set Negative number Descriptive statistics Amenable group Link (knot theory) Constraint (mathematics) Theory of relativity Block (periodic table) Sampling (statistics) Infinity Parameter (computer programming) Sequence Category of being Arithmetic mean Sample (statistics) Lattice (order) Angle Order (biology) Phase transition Queue (abstract data type) Point (geometry) Slide rule Standard error Distribution (mathematics) Letterpress printing Similarity (geometry) Valuation (algebra) Student's t-test Average Graph (mathematics) Event horizon Estimator Open set Number Frequency Goodness of fit Coefficient Spectral method Energy level Units of measurement Scale (map) Series (mathematics) Statistical hypothesis testing Standard deviation Chemical equation Mathematical model Set (mathematics) Quadratic form Local Group Perspective (visual) Field extension Estimation Function (mathematics) Network topology Universe (mathematics) Noise Social class Mathematical optimization Matrix (mathematics) Gradient descent Musical ensemble State of matter Multiplication sign Sheaf (mathematics) 1 (number) Insertion loss Parameter (computer programming) Mereology Food energy Grothendieck topology Order (biology) Mathematics Matrix (mathematics) Many-sorted logic Phase transition Statistics Arrow of time Area Linear regression Moment (mathematics) Knot Connected space Proof theory Sparse matrix Vector space Hausdorff dimension Normal (geometry) Right angle Energy level Block (periodic table) Resultant Sinc function Combinatorics Metre Geometry Statistics Link (knot theory) Divisor Parity (mathematics) Sparse matrix Distance Power (physics) Natural number Average Reduction of order Subtraction Addition Element (mathematics) Bound state Mathematical analysis Incidence algebra Axialer Vektor Estimator Database normalization Commutator Dependent and independent variables Object (grammar) Coefficient Local ring Spectrum (functional analysis)
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