13 research outputs found
A Unified Approach to Learning Ising Models: Beyond Independence and Bounded Width
We revisit the problem of efficiently learning the underlying parameters of
Ising models from data. Current algorithmic approaches achieve essentially
optimal sample complexity when given i.i.d. samples from the stationary measure
and the underlying model satisfies "width" bounds on the total
interaction involving each node. We show that a simple existing approach based
on node-wise logistic regression provably succeeds at recovering the underlying
model in several new settings where these assumptions are violated:
(1) Given dynamically generated data from a wide variety of local Markov
chains, like block or round-robin dynamics, logistic regression recovers the
parameters with optimal sample complexity up to factors. This
generalizes the specialized algorithm of Bresler, Gamarnik, and Shah [IEEE
Trans. Inf. Theory'18] for structure recovery in bounded degree graphs from
Glauber dynamics.
(2) For the Sherrington-Kirkpatrick model of spin glasses, given
independent samples, logistic regression recovers the
parameters in most of the known high-temperature regime via a simple reduction
to weaker structural properties of the measure. This improves on recent work of
Anari, Jain, Koehler, Pham, and Vuong [ArXiv'23] which gives distribution
learning at higher temperature.
(3) As a simple byproduct of our techniques, logistic regression achieves an
exponential improvement in learning from samples in the M-regime of data
considered by Dutt, Lokhov, Vuffray, and Misra [ICML'21] as well as novel
guarantees for learning from the adversarial Glauber dynamics of Chin, Moitra,
Mossel, and Sandon [ArXiv'23].
Our approach thus significantly generalizes the elegant analysis of Wu,
Sanghavi, and Dimakis [Neurips'19] without any algorithmic modification.Comment: 51 page
Eigenstripping, Spectral Decay, and Edge-Expansion on Posets
Fast mixing of random walks on hypergraphs (simplicial complexes) has recently led to myriad breakthroughs throughout theoretical computer science. Many important applications, however, (e.g. to LTCs, 2-2 games) rely on a more general class of underlying structures called posets, and crucially take advantage of non-simplicial structure. These works make it clear that the global expansion properties of posets depend strongly on their underlying architecture (e.g. simplicial, cubical, linear algebraic), but the overall phenomenon remains poorly understood. In this work, we quantify the advantage of different poset architectures in both a spectral and combinatorial sense, highlighting how regularity controls the spectral decay and edge-expansion of corresponding random walks.
We show that the spectra of walks on expanding posets (Dikstein, Dinur, Filmus, Harsha APPROX-RANDOM 2018) concentrate in strips around a small number of approximate eigenvalues controlled by the regularity of the underlying poset. This gives a simple condition to identify poset architectures (e.g. the Grassmann) that exhibit strong (even exponential) decay of eigenvalues, versus architectures like hypergraphs whose eigenvalues decay linearly - a crucial distinction in applications to hardness of approximation and agreement testing such as the recent proof of the 2-2 Games Conjecture (Khot, Minzer, Safra FOCS 2018). We show these results lead to a tight characterization of edge-expansion on expanding posets in the ??-regime (generalizing recent work of Bafna, Hopkins, Kaufman, and Lovett (SODA 2022)), and pay special attention to the case of the Grassmann where we show our results are tight for a natural set of sparsifications of the Grassmann graphs. We note for clarity that our results do not recover the characterization of expansion used in the proof of the 2-2 Games Conjecture which relies on ?_? rather than ??-structure
Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence
Online advertising via auctions increasingly dominates the marketing landscape. A typical advertiser may participate in thousands of auctions each day with bids tailored to a variety of signals about user demographics and intent. These auctions are strategically linked through a global budget constraint. To help address the difficulty of bidding, many major online platforms now provide automated budget management via a flexible approach called budget pacing: rather than bidding directly, an advertiser specifies a global budget target and a maximum willingness-to-pay for different types of advertising opportunities. The specified maximums are then scaled down (or "paced") by a multiplier so that the realized total spend matches the target budget.
These automated bidders are now near-universally adopted across all mature advertising platforms, raising pressing questions about market outcomes that arise when advertisers use budget pacing simultaneously. In this paper we study the aggregate welfare and individual regret guarantees of dynamic pacing algorithms in repeated auctions with budgets. We show that when agents simultaneously use a natural form of gradient-based pacing, the liquid welfare obtained over the course of the dynamics is at least half the optimal liquid welfare obtainable by any allocation rule, matching the best possible bound for static auctions even in pure Nash equilibria [Aggarwal et al., WINE 2019; Babaioff et al., ITCS 2021]. In contrast to prior work, these results hold without requiring convergence of the dynamics, circumventing known computational obstacles of finding equilibria [Chen et al., EC 2021]. Our result is robust to the correlation structure among agents\u27 valuations and holds for any core auction, a broad class that includes first-price, second-price, and GSP auctions. We complement the aggregate guarantees by showing that an agent using such pacing algorithms achieves an O(T^{3/4}) regret relative to the value obtained by the best fixed pacing multiplier in hindsight in stochastic bidding environments. Compared to past work, this result applies to more general auctions and extends to adversarial settings with respect to dynamic regret
Fractional Pseudorandom Generators from Any Fourier Level
We prove new results on the polarizing random walk framework introduced in
recent works of Chattopadhyay {et al.} [CHHL19,CHLT19] that exploit
Fourier tail bounds for classes of Boolean functions to construct pseudorandom
generators (PRGs). We show that given a bound on the -th level of the
Fourier spectrum, one can construct a PRG with a seed length whose quality
scales with . This interpolates previous works, which either require Fourier
bounds on all levels [CHHL19], or have polynomial dependence on the error
parameter in the seed length [CHLT10], and thus answers an open question in
[CHLT19]. As an example, we show that for polynomial error, Fourier bounds on
the first levels is sufficient to recover the seed length in
[CHHL19], which requires bounds on the entire tail.
We obtain our results by an alternate analysis of fractional PRGs using
Taylor's theorem and bounding the degree- Lagrange remainder term using
multilinearity and random restrictions. Interestingly, our analysis relies only
on the \emph{level-k unsigned Fourier sum}, which is potentially a much smaller
quantity than the notion in previous works. By generalizing a connection
established in [CHH+20], we give a new reduction from constructing PRGs to
proving correlation bounds. Finally, using these improvements we show how to
obtain a PRG for polynomials with seed length close to the
state-of-the-art construction due to Viola [Vio09], which was not known to be
possible using this framework
Eigenstripping, Spectral Decay, and Edge-Expansion on Posets
Fast mixing of random walks on hypergraphs has led to myriad breakthroughs in
theoretical computer science in the last five years. On the other hand, many
important applications (e.g. to locally testable codes, 2-2 games) rely on a
more general class of underlying structures called posets, and crucially take
advantage of non-simplicial structure. These works make it clear the global
expansion properties of posets depend strongly on their underlying architecture
(e.g. simplicial, cubical, linear algebraic), but the overall phenomenon
remains poorly understood. In this work, we quantify the advantage of different
poset architectures in both a spectral and combinatorial sense, highlighting
how regularity controls the spectral decay and edge-expansion of corresponding
random walks.
We show that the spectra of walks on expanding posets (Dikstein, Dinur,
Filmus, Harsha APPROX-RANDOM 2018) concentrate in strips around a small number
of approximate eigenvalues controlled by the regularity of the underlying
poset. This gives a simple condition to identify poset architectures (e.g. the
Grassmann) that exhibit exponential decay of eigenvalues, versus architectures
like hypergraphs whose eigenvalues decay linearly -- a crucial distinction in
applications to hardness of approximation such as the recent proof of the 2-2
Games Conjecture (Khot, Minzer, Safra FOCS 2018). We show these results lead to
a tight characterization of edge-expansion on posets in the -regime
(generalizing recent work of Bafna, Hopkins, Kaufman, and Lovett (SODA 2022)),
and pay special attention to the case of the Grassmann where we show our
results are tight for a natural set of sparsifications of the Grassmann graphs.
We note for clarity that our results do not recover the characterization of
expansion used in the proof of the 2-2 Games Conjecture which relies on
rather than -structure
Reformulating a Pharmacophore for 5âHT<sub>2A</sub> Serotonin Receptor Antagonists
Several
pharmacophore models have been proposed for 5-HT<sub>2A</sub> serotonin
receptor antagonists. These typically consist of two aromatic/hydrophobic
moieties separated by a given distance from each other, and from a
basic amine. Although specified distances might vary, the models are
relatively similar in their general construction. Because our preliminary
data indicated that two aromatic (hydrophobic) moieties might not
be required for such action, we deconstructed the serotonin-dopamine
antipsychotic agent risperidone (<b>1</b>) into four smaller
structural fragments that were thoroughly examined in 5-HT<sub>2A</sub> receptor binding and functional (i.e., two-electrode voltage clamp
(TEVC) and intracellular calcium release) assays. It was apparent
that truncated risperidone analogues behaved as antagonists. In particular,
6-fluoro-3-(1-methylpiperidin-4-yl)Âbenzisoxazole (<b>4</b>)
displayed high affinity for 5-HT<sub>2A</sub> receptors (<i>K</i><sub>i</sub> of ca. 12 nM) relative to risperidone (<i>K</i><sub>i</sub> of ca. 5 nM) and behaved as a potent 5-HT<sub>2A</sub> serotonin receptor antagonist. These results suggest that multiple
aromatic (hydrophobic) moieties are <i>not</i> essential
for high-affinity 5-HT<sub>2A</sub> receptor binding and antagonist
activity and that current pharmacophore models for such agents are
very much in need of revision