Filtration and filtered probability space

Depends on

• Probability measures and probability spaces
• Sigma-algebras

Used by

• Empirical-Bernstein confidence-sequence interval update Algorithm
• Minibatch stochastic gradient descent Algorithm
• Sequential likelihood-ratio test Algorithm
• Stochastic gradient descent Algorithm
• A supermartingale supremum threshold need not be attained Counterexample
• Validity under one null law does not give a composite-null test supermartingale Counterexample
• Adapted and integrable stochastic process Definition
• Anytime-valid p-value processes Definition
• Bandit importance-weighted estimator Definition
• Conditionally sub-Gaussian increments Definition
• Confidence sequence for a time-varying target Definition
• Confidence sequences Definition
• Contextual bandit protocol with finite expert advice Definition
• Discrete stopping time Definition
• Filtration-adapted stochastic-gradient oracles and Robbins–Monro updates Definition
• Finite-dimensional linear contextual bandit model Definition
• Nonnegative test supermartingales Definition
• One-sided sub-exponential uniform boundary Definition
• Predictable discrete time process Definition
• Reverse filtration and reverse martingale Definition
• Time-homogeneous Markov chain with transition kernel Definition
• A finite-horizon likelihood-ratio test supermartingale Example
• Constant-step SGD can have a nonzero noise floor Example
• One streaming least-squares SGD update Example
• Uniform empirical-risk sampling gives an unbiased bounded-variance gradient Example
• Client drift under FedAvg gradient dissimilarity Lemma
• Concentration for adaptively sampled MDP observations Lemma
• Conditional moments of the bandit importance-weighted estimator Lemma
• Convex SCAFFOLD client-drift bound Lemma
• Convex SCAFFOLD server-update second moment Lemma
• Coordinate-wise stochastic approximation converges to a contraction fixed point Lemma
• Discrete stochastic local-to-global RMS stability bound Lemma
• Martingale differences are orthogonal in l2 Lemma
• Nonconvex SCAFFOLD control-anchor tracking recursion Lemma
• Nonconvex SCAFFOLD progress in one communication round Lemma
• Nonconvex SCAFFOLD query-point drift bound Lemma
• Nonconvex SCAFFOLD server-update moments Lemma
• One-round progress of strongly convex FedAvg Lemma
• Option II controls track gradients at stored client anchors Lemma
• Predictably weighted bounded martingale differences have a convergent series Lemma

…and 18 more results.

Dependency tree · two levels

5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• van der Vaart, Martingales, Diffusions and Financial Mathematics (standard reference, not scraped)