\u00a9 2023 Owner/Author(s).
", "abstract": "In a misspecified social learning setting, agents are condescending if they perceive their peers as having private information that is of lower quality than it is in reality. Applying this to a standard sequential model, we show that outcomes improve when agents are mildly condescending. In contrast, too much condescension leads to worse outcomes, as does anti-condescension.
", "date": "2023-07", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "119", "isbn": "9798400701047", "book_title": "EC '23: Proceedings of the 24th ACM Conference on Economics and Computation", "official_url": "https://authors.library.caltech.edu/records/jhp7z-fw809", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1944153" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1145/3580507.3597752", "primary_object": { "basename": "3580507.3597752.pdf", "url": "https://authors.library.caltech.edu/records/jhp7z-fw809/files/3580507.3597752.pdf" }, "pub_year": "2023", "author_list": "Arieli, Itai; Babichenkoyako, Yakov; et al." }, { "id": "https://authors.library.caltech.edu/records/jvfeg-gne85", "eprint_status": "archive", "datestamp": "2026-01-15 00:36:11", "lastmod": "2026-03-28 03:49:58", "type": "conference_item", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Park", "given": "Jinyoung" }, "orcid": "0000-0003-3962-5668" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "A Proof of the Kahn-Kalai Conjecture", "ispublished": "pub", "full_text_status": "public", "abstract": "Proving the \"expectation-threshold\" conjecture of Kahn and Kalai, we show that for any increasing property $\\mathcal{F}$ on a finite set X, \\begin{equation*}p_{c}(\\mathcal{F})=O(q(\\mathcal{F})\\log\\ell(\\mathcal{F})),\\end{equation*} where $p_{c}(\\mathcal{F})$ and $q(\\mathcal{F})$ are the threshold and \"expectation threshold\" of $\\mathcal{F}$, and $\\ell(\\mathcal{F})$ is the maximum size of a minimal member of $\\mathcal{F}$.", "date": "2022-10", "date_type": "published", "publication": "2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)", "publisher": "IEEE", "pagerange": "636-639", "official_url": "https://authors.library.caltech.edu/records/jvfeg-gne85", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/focs54457.2022.00066", "pub_year": "2022", "author_list": "Park, Jinyoung and Pham, Huy Tuan" }, { "id": "https://authors.library.caltech.edu/records/kt7jj-7nn90", "eprint_status": "archive", "datestamp": "2026-01-15 00:36:18", "lastmod": "2026-03-28 03:49:03", "type": "conference_item", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Anari", "given": "Nima" }, "orcid": "0000-0002-4394-3530" }, { "name": { "family": "Jain", "given": "Vishesh" }, "orcid": "0000-0002-7275-3218" }, { "name": { "family": "Koehler", "given": "Frederic" }, "orcid": "0000-0001-5220-9680" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Vuong", "given": "Thuy-Duong" }, "orcid": "0000-0003-0271-9687" } ] }, "title": "Entropic independence: optimal mixing of down-up random walks", "ispublished": "pub", "full_text_status": "public", "abstract": "We introduce a notion called entropic independence that is an entropic analog of spectral notions of high-dimensional expansion. Informally, entropic independence of a background distribution \u00b5 on k-sized subsets of a ground set of elements says that for any (possibly randomly chosen) set S, the relative entropy of a single element of S drawn uniformly at random carries at most O(1/k) fraction of the relative entropy of S. Entropic independence is the analog of the notion of spectral independence, if one replaces variance by entropy. We use entropic independence to derive tight mixing time bounds, overcoming the lossy nature of spectral analysis of Markov chains on exponential-sized state spaces. In our main technical result, we show a general way of deriving entropy contraction, a.k.a. modified log-Sobolev inequalities, for down-up random walks from spectral notions. We show that spectral independence of a distribution under arbitrary external fields automatically implies entropic independence. We furthermore extend our theory to the case where spectral independence does not hold under arbitrary external fields. To do this, we introduce a framework for obtaining tight mixing time bounds for Markov chains based on what we call restricted modified log-Sobolev inequalities, which guarantee entropy contraction not for all distributions, but for those in a sufficiently large neighborhood of the stationary distribution. To derive our results, we relate entropic independence to properties of polynomials: \u00b5 is entropically independent exactly when a transformed version of the generating polynomial of \u00b5 is upper bounded by its linear tangent; this property is implied by concavity of the said transformation, which was shown by prior work to be locally equivalent to spectral independence. We apply our results to obtain (1) tight modified log-Sobolev inequalities and mixing times for multi-step down-up walks on fractionally log-concave distributions, (2) the tight mixing time of O(nlogn) for Glauber dynamics on Ising models whose interaction matrix has eigenspectrum lying within an interval of length smaller than 1, improving upon the prior quadratic dependence on n, and (3) nearly-linear time O\u03b4(n) samplers for the hardcore and Ising models on n-node graphs that have \u03b4-relative gap to the tree-uniqueness threshold. In the last application, our bound on the running time does not depend on the maximum degree \u0394 of the graph, and is therefore optimal even for high-degree graphs, and in fact, is sublinear in the size of the graph for high-degree graphs.", "date": "2022-06-09", "date_type": "published", "publication": "Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing", "publisher": "ACM", "pagerange": "1418-1430", "official_url": "https://authors.library.caltech.edu/records/kt7jj-7nn90", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1145/3519935.3520048", "pub_year": "2022", "author_list": "Anari, Nima; Jain, Vishesh; et al." }, { "id": "https://authors.library.caltech.edu/records/g1cd6-4aq79", "eprint_status": "archive", "datestamp": "2026-01-15 00:36:38", "lastmod": "2026-03-28 03:48:35", "type": "conference_item", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Jain", "given": "Vishesh" }, "orcid": "0000-0002-7275-3218" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Vuong", "given": "Thuy Duong" }, "orcid": "0000-0003-0271-9687" } ] }, "title": "Towards the sampling Lov\u00e1sz Local Lemma", "ispublished": "pub", "full_text_status": "public", "abstract": "Let $\\Phi=(V, \\mathcal{C})$ be a constraint satisfaction problem on variables $v_{1}, \\ldots, v_{n}$ such that each constraint depends on at most $k$ variables and such that each variable assumes values in an alphabet of size at most [$q$]. Suppose that each constraint shares variables with at most $\\Delta$ constraints and that each constraint is violated with probability at most $p$ (under the product measure on its variables). We show that for $k, q=O(1)$, there is a deterministic, polynomial time algorithm to approximately count the number of satisfying assignments and a randomized, polynomial time algorithm to sample from approximately the uniform distribution on satisfying assignments, provided that $C\\cdot q^{2}\\cdot k\\cdot p\\cdot\\Delta^{7} < 1$, where $C$ is an absolute constant. Previously, a result of this form was known essentially only in the special case when each constraint is violated by exactly one assignment to its variables. For the special case of $k$ .CNF formulas, the term $\\Delta^{7}$ improves the previously best known $\\Delta^{60}$ for deterministic algorithms [Moitra, J.ACM, 2019] and $\\Delta^{13}$ for randomized algorithms [Feng, Guo, Yin, and Zhang, STOC 2021]. For the special case of properly $q$-coloring $k$-uniform hypergraphs, the term $\\Delta^{7}$ improves the previously best known $\\Delta^{14}$ for deterministic algorithms [Guo, Liao, Lu, and Zhang, SICOMP, 2019] and $\\Delta^{9}$ for randomized algorithms [Feng, Guo, Yin, and Zhang, STOC 2021].", "date": "2022-02", "date_type": "published", "publication": "2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)", "publisher": "IEEE", "pagerange": "173-183", "official_url": "https://authors.library.caltech.edu/records/g1cd6-4aq79", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/focs52979.2021.00025", "pub_year": "2022", "author_list": "Jain, Vishesh; Pham, Huy Tuan; et al." } ]