Asymptotic evaluation of certain Markov process expectations for large time

By M. Donsker, S. Varadhan. 1975

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Citations in the corpus

Mutual Information Neural Estimation (2018, methodology): “A key technical ingredient of MINE are dual representations of the KL-divergence.”
Formal Limitations on the Measurement of Mutual Information (2018, background): “UES WITH THE DONSKER-VARADHAN LOWER BOUND The Donsker-Varadhan (DV) lower bound on KL divergence is stated below. For completeness, a simple proof is given in the supplementary material. Theorem 2.1 (Donsker and Varadhan, 1983). Let p Xand q Xbe distributions over Xwith ﬁnite KL divergence. Then for”
Imitation Learning via Off-Policy Distribution Matching (2019, methodology): “However, in contrast to the form used in Equation 4 or 5, we use the Donsker-Varadhan representation (Donsker & Varadhan, 1983) given by, s,a ) ] − E ( s,a ) ∼ d π [ x ( s, a )] .”
Obfuscation via Information Density Estimation (2019, methodology): “TIDE is based on a variational representation of KL divergence1 known as the Donsker-Varadhan (DV) representation (Donsker and Varadhan, 1983), given by DKL(PS,X‖PSPX) = sup g:S×X→R {EPS,X [g(S,X)]− logEPSPX [eg(S,X)]}.”
Multi-label Contrastive Predictive Coding (2020, methodology): “CPC would tend to underestimate the density ratio (since it is capped at m) and generally requires O(e ) samples to achieve low bias; MINE [3] (based on the Donsker-Varadhan inequality [14]) is a biased estimator and requires O(e ) samples to achieve low variance [44, 43].”
Factorizing Knowledge in Neural Networks (2022, methodology): “We substitute q(y|x) into Equation 9 and derive an unnormalized lower bound on MI, which we refer to as IUBA for the Barber and Agakov bound [1] and IDA Donsker & Varadhan bound [6].”
A Course on Large Deviations With an Introduction to Gibbs Measures (2015, background): “A uniformity condition can also be formulated for Polish spaces ([25, 33], Section 6.”
User-friendly introduction to PAC-Bayes bounds (2021, background): “Apply Fubini: ESEθ∼π [ eλ[r(θ)−R(θ)] ] ≤ eλ 2C2 8n and then Donsker and Varadhan’s variational formula (Lemma 2.2): ES [ esupρ∈P(Θ) λEθ∼ρ[r(θ)−R(θ)]−KL(ρ‖π) ] ≤ eλ 2C2 8n .”
On large deviations of coupled diffusions with time scale separation (2013, background): “tup of the averaging principle where C(u,x) = 0. The LDP for the empirical measures of continuous-time Markov processes, such as in Corollary 2.3, is a well explored subject, see Donsker and Varadhan [13, 14], Deuschel and Stroock [12]. The canonical form of the large deviation rate function is supf”
Bridging the Gap Between $f$-GANs and Wasserstein GANs (2019, background): “First, we show that Proposition 2 directly implies the DonskerVaradhan inequality (Donsker and Varadhan, 1975).”
Smooth Ambiguity Aversion toward Small Risks and Continuous-Time Recursive Utility (2013, background): “A variational identity of Donsker and Varadhan (1975) (which is also a corollary of Proposition 8 of Section 3.”
Lifelong Learning with Non-i.i.d. Tasks (2015, unknown): “By applying Donsker-Varadhan’s variational formula [15] one obtains that: er(Q)− ẽr(Q) ≤ 1 λ ( KL(Q||P) + logEA∼P expλ ( er(A)− 1 n− 1 n ∑”
Generalized Energy Based Models (2020, background): “When the Kullback-Leibler divergence between P and G is well defined, (5) corresponds to the Donsker-Varadhan (DV) lower bound on the KL (Donsker and Varadhan, 1975), meaning that KL(P||G)≥LP,G(E) for allE, with equality only whenE is the negative log-density ratio of P w.”