Matches in SemOpenAlex for { <https://semopenalex.org/work/W4380490510> ?p ?o ?g. }
- W4380490510 abstract "We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high-dimensional Bayesian model. We show that for any signal strength λ>1 (the weak-recovery threshold), there exists a unique local minimizer of the TAP free energy functional near the mean of the Bayes posterior law. Furthermore, the TAP free energy in a local neighborhood of this minimizer is strongly convex. Consequently, a natural-gradient/mirror-descent algorithm achieves linear convergence to this minimizer from a local initialization, which may be obtained by a constant number of iterations of Approximate Message Passing (AMP). This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy. We also analyze the finite-sample convergence of AMP, showing that AMP is asymptotically stable at the TAP minimizer for any λ>1, and is linearly convergent to this minimizer from a spectral initialization for sufficiently large λ. Such a guarantee is stronger than results obtainable by state evolution analyses, which only describe a fixed number of AMP iterations in the infinite-sample limit. Our proofs combine the Kac–Rice formula and Sudakov–Fernique Gaussian comparison inequality to analyze the complexity of critical points that satisfy strong convexity and stability conditions within their local neighborhoods." @default.
- W4380490510 created "2023-06-14" @default.
- W4380490510 creator A5047187143 @default.
- W4380490510 creator A5050590699 @default.
- W4380490510 creator A5057617652 @default.
- W4380490510 date "2023-04-01" @default.
- W4380490510 modified "2023-10-16" @default.
- W4380490510 title "Local convexity of the TAP free energy and AMP convergence for Z2-synchronization" @default.
- W4380490510 cites W142487310 @default.
- W4380490510 cites W1483883706 @default.
- W4380490510 cites W1520752838 @default.
- W4380490510 cites W1555319958 @default.
- W4380490510 cites W1625271478 @default.
- W4380490510 cites W1970789124 @default.
- W4380490510 cites W1984830458 @default.
- W4380490510 cites W1985868645 @default.
- W4380490510 cites W1990755770 @default.
- W4380490510 cites W2000116444 @default.
- W4380490510 cites W2016384870 @default.
- W4380490510 cites W2040745222 @default.
- W4380490510 cites W2040969041 @default.
- W4380490510 cites W2048717141 @default.
- W4380490510 cites W2052076819 @default.
- W4380490510 cites W2066459155 @default.
- W4380490510 cites W2067038358 @default.
- W4380490510 cites W2069097920 @default.
- W4380490510 cites W2069754508 @default.
- W4380490510 cites W2078703947 @default.
- W4380490510 cites W2082029531 @default.
- W4380490510 cites W2090980101 @default.
- W4380490510 cites W2093550824 @default.
- W4380490510 cites W2101794336 @default.
- W4380490510 cites W2120340025 @default.
- W4380490510 cites W2129397584 @default.
- W4380490510 cites W2138556224 @default.
- W4380490510 cites W2143703915 @default.
- W4380490510 cites W2166670884 @default.
- W4380490510 cites W2174706414 @default.
- W4380490510 cites W2174754147 @default.
- W4380490510 cites W2216459995 @default.
- W4380490510 cites W2332917886 @default.
- W4380490510 cites W2410802601 @default.
- W4380490510 cites W2535496140 @default.
- W4380490510 cites W2538202101 @default.
- W4380490510 cites W2551153860 @default.
- W4380490510 cites W2564257896 @default.
- W4380490510 cites W2565889208 @default.
- W4380490510 cites W2588219153 @default.
- W4380490510 cites W2612481336 @default.
- W4380490510 cites W2742398704 @default.
- W4380490510 cites W2945463326 @default.
- W4380490510 cites W2962804724 @default.
- W4380490510 cites W2963064298 @default.
- W4380490510 cites W2963072996 @default.
- W4380490510 cites W2963122491 @default.
- W4380490510 cites W2963206527 @default.
- W4380490510 cites W2963305853 @default.
- W4380490510 cites W2963698262 @default.
- W4380490510 cites W2963742450 @default.
- W4380490510 cites W2963886912 @default.
- W4380490510 cites W2964102258 @default.
- W4380490510 cites W2964282092 @default.
- W4380490510 cites W2964312599 @default.
- W4380490510 cites W2965130990 @default.
- W4380490510 cites W2968353065 @default.
- W4380490510 cites W2974583905 @default.
- W4380490510 cites W3010359926 @default.
- W4380490510 cites W3015328986 @default.
- W4380490510 cites W3029292097 @default.
- W4380490510 cites W3033456699 @default.
- W4380490510 cites W3043271774 @default.
- W4380490510 cites W3049347563 @default.
- W4380490510 cites W3087561124 @default.
- W4380490510 cites W3088535225 @default.
- W4380490510 cites W3097770378 @default.
- W4380490510 cites W3098468003 @default.
- W4380490510 cites W3098848552 @default.
- W4380490510 cites W3100193873 @default.
- W4380490510 cites W3101380508 @default.
- W4380490510 cites W3101522767 @default.
- W4380490510 cites W3103647971 @default.
- W4380490510 cites W3103929211 @default.
- W4380490510 cites W3104163199 @default.
- W4380490510 cites W3105163160 @default.
- W4380490510 cites W3105662517 @default.
- W4380490510 cites W3113425034 @default.
- W4380490510 cites W3118365541 @default.
- W4380490510 cites W3125452207 @default.
- W4380490510 cites W3125529942 @default.
- W4380490510 cites W3126400887 @default.
- W4380490510 cites W3140735157 @default.
- W4380490510 cites W3158809943 @default.
- W4380490510 cites W3202433451 @default.
- W4380490510 cites W4210755813 @default.
- W4380490510 cites W4292482091 @default.
- W4380490510 cites W4300570305 @default.
- W4380490510 cites W4313227414 @default.
- W4380490510 doi "https://doi.org/10.1214/23-aos2257" @default.
- W4380490510 hasPublicationYear "2023" @default.
- W4380490510 type Work @default.