arXiv subjects

Himanshu Tyagi

Publications and source records attributed to Himanshu Tyagi.

At least 37 records · Page 2Linked to original sources

arXiv2024

Proof of Diligence: Cryptoeconomic Security for Rollups

Layer 1 (L1) blockchains such as Ethereum are secured under an "honest supermajority of stake" assumption for a large pool of validators who verify each and every transaction on it. This high security comes at a scalability cost which not only effects the throughput of the blockchain but also results in high gas fees for executing transactions on chain. The most successful solution for this problem is provided by optimistic rollups, Layer 2 (L2) blockchains that execute transactions outside L1 but post the transaction data on L1. The security for such L2 chains is argued, informally, under the assumption that a set of nodes will check the transaction data posted on L1 and raise an alarm (a fraud proof) if faulty transactions are detected. However, all current deployments lack a proper incentive mechanism for ensuring that these nodes will do their job ``diligently'', and simply rely on a cursory incentive alignment argument for security. We solve this problem by introducing an incentivized watchtower network designed to serve as the first line of defense for rollups. Our main contribution is a ``Proof of Diligence'' protocol that requires watchtowers to continuously provide a proof that they have verified L2 assertions and get rewarded for the same. Proof of Diligence protocol includes a carefully-designed incentive mechanism that is provably secure when watchtowers are rational actors, under a mild rational independence assumption.

cs.CR↗

arXiv2024

Host star properties of hot, warm and cold Jupiters in the solar neighborhood from \textit{Gaia} DR3: clues to formation pathways

Giant planets exhibit diverse orbital properties, hinting at their distinct formation and dynamic histories. In this paper, using $\textit{Gaia}$ DR3, we investigate if and how the orbital properties of Jupiters are linked to their host star properties, particularly their metallicity and age. We obtain metallicities for main sequence stars of spectral type F, G, and K, hosting hot, warm, and cold Jupiters with varying eccentricities. We compute the velocity dispersion of host stars of these three groups using kinematic information from $\textit{Gaia}$ DR3 and obtain average ages using velocity dispersion-age relation. We find that host stars of hot Jupiters are relatively metal-rich ([Fe/H]=$0.18 \pm 0.13$) and young ( median age $3.97 \pm 0.51$ Gyr) compared to the host stars of cold Jupiters in nearly circular orbits, which are relatively metal-poor ($0.03 \pm 0.18$) and older (median age $6.07 \pm 0.79$ Gyr). Host stars of cold Jupiters in high eccentric orbits, on the other hand, show metallicities similar to that of the hosts of hot Jupiters, but are older, on average (median age $6.25 \pm 0.92$ Gyr). The similarity in metallicity between hosts of hot Jupiters and hosts of cold Jupiters in high eccentric orbits supports high eccentricity migration as the potential origin of hot Jupiters, with the latter serving as the progenitors. However, the average age difference between them suggests that the older hot Jupiters may have been engulfed by the star in a timescale of $\sim 6$ Gyr. This allows us to estimate the value of stellar tidal quality factor $Q'_\ast\sim10^{6\pm1}$.

astro-ph.EP↗

arXiv2024

Investigating Protostellar Accretion-Driven Outflows Across the Mass Spectrum: JWST NIRSpec IFU 3-5~$μ$m Spectral Mapping of Five Young Protostars

Investigating Protostellar Accretion is a Cycle 1 JWST program using the NIRSpec+MIRI integral field units to obtain 2.9--28 $μ$m spectral cubes of five young protostars with luminosities of 0.2-10,000 L$_{\odot}$ in their primary accretion phase. This paper introduces the NIRSpec 2.9--5.3 $μ$m data of the inner 840-9000 au with spatial resolutions from 28-300 au. The spectra show rising continuum emission; deep ice absorption; emission from H$_{2}$, H~I, and [Fe~II]; and the CO fundamental series in emission and absorption. Maps of the continuum emission show scattered light cavities for all five protostars. In the cavities, collimated jets are detected in [Fe~II] for the four $< 320$~L$_{\odot}$ protostars, two of which are additionally traced in Br-$α$. Knots of [Fe~II] emission are detected toward the most luminous protostar, and knots of [FeII] emission with dynamical times of $< 30$~yrs are found in the jets of the others. While only one jet is traced in H$_2$, knots of H$_2$ and CO are detected in the jets of four protostars. H$_2$ is seen extending through the cavities, showing that they are filled by warm molecular gas. Bright H$_2$ emission is seen along the walls of a single cavity, while in three cavities narrow shells of H$_2$ emission are found, one of which has an [Fe~II] knot at its apex. These data show cavities containing collimated jets traced in atomic/ionic gas surrounded by warm molecular gas in a wide-angle wind and/or gas accelerated by bow shocks in the jets.

astro-ph.SR↗

arXiv2024

JWST detections of amorphous and crystalline HDO ice toward massive protostars

This work aims to utilize the increased sensitivity and resolution of the JWST to quantify the HDO/H$_{2}$O ratio in ices toward young stellar objects (YSOs) and to determine if the HDO/H$_{2}$O ratios measured in the gas phase toward massive YSOs (MYSOs) are representative of the ratios in their ice envelopes. Two protostars observed in the Investigating Protostellar Accretion (IPA) program using JWST NIRSpec were analyzed: HOPS 370, an intermediate-mass YSO (IMYSO), and IRAS 20126+4104, a MYSO. The HDO ice toward these sources was detected above the 3$σ$ level and quantified via its 4.1 $μ$m band. The contributions from the CH$_{3}$OH combination modes to the observed optical depth in this spectral region were constrained via the CH$_{3}$OH 3.53 $μ$m band to ensure that the integrated optical depth of the HDO feature was not overestimated. H$_{2}$O ice was quantified via its 3 $μ$m band. From these fits, ice HDO/H$_{2}$O abundance ratios of 4.6$\pm$1.8$\times$10$^{-3}$ and 2.6$\pm$1.2$\times$10$^{-3}$ are obtained for HOPS 370 and IRAS 20126+4104, respectively. The simultaneous detections of both crystalline HDO and crystalline H$_{2}$O corroborate the assignment of the observed feature at 4.1 $μ$m to HDO ice. The ice HDO/H$_{2}$O ratios are similar to the highest reported gas HDO/H$_{2}$O ratios measured toward MYSOs as well as the hot inner regions of isolated low-mass protostars, suggesting that at least some of the gas HDO/H$_{2}$O ratios measured toward massive hot cores are representative of the HDO/H$_{2}$O ratios in ices. The need for an H$_{2}$O-rich CH$_{3}$OH component in the CH$_{3}$OH ice analysis supports recent experimental and observational results that indicate that some CH$_{3}$OH ice may form prior to the CO freeze-out stage in H$_{2}$O-rich ice layers.

astro-ph.SR↗

arXiv2024

JWST/MIRI detection of suprathermal OH rotational emissions: probing the dissociation of the water by Lyman alpha photons near the protostar HOPS 370

Using the MIRI/MRS spectrometer on JWST, we have detected pure rotational, suprathermal OH emissions from the vicinity of the intermediate-mass protostar HOPS 370 (OMC2/FIR3). These emissions are observed from shocked knots in a jet/outflow, and originate in states of rotational quantum number as high as 46 that possess excitation energies as large as $E_U/k = 4.65 \times 10^4$ K. The relative strengths of the observed OH lines provide a powerful diagnostic of the ultraviolet radiation field in a heavily-extinguished region ($A_V \sim 10 - 20$) where direct UV observations are impossible. To high precision, the OH line strengths are consistent with a picture in which the suprathermal OH states are populated following the photodissociation of water in its $\tilde B - X$ band by ultraviolet radiation produced by fast ($\sim 80\,\rm km\,s^{-1}$) shocks along the jet. The observed dominance of emission from symmetric ($A^\prime$) OH states over that from antisymmetric ($A^{\prime\prime}$) states provides a distinctive signature of this particular population mechanism. Moreover, the variation of intensity with rotational quantum number suggests specifically that Ly$α$ radiation is responsible for the photodissociation of water, an alternative model with photodissociation by a 10$^4$ K blackbody being disfavored at a high level of significance. Using measurements of the Br$α$ flux to estimate the Ly$α$ production rate, we find that $\sim 4\%$ of the Ly$α$ photons are absorbed by water. Combined with direct measurements of water emissions in the $ν_2 = 1 -0$ band, the OH observations promise to provide key constraints on future models for the diffusion of Ly$α$ photons in the vicinity of a shock front.

astro-ph.GA↗

arXiv2024

BFT-PoLoc: A Byzantine Fortified Trigonometric Proof of Location Protocol using Internet Delays

Internet platforms depend on accurately determining the geographical locations of online users to deliver targeted services (e.g., advertising). The advent of decentralized platforms (blockchains) emphasizes the importance of geographically distributed nodes, making the validation of locations more crucial. In these decentralized settings, mutually non-trusting participants need to {\em prove} their locations to each other. The incentives for claiming desired location include decentralization properties (validators of a blockchain), explicit rewards for improving coverage (physical infrastructure blockchains) and regulatory compliance -- and entice participants towards prevaricating their true location malicious via VPNs, tampering with internet delays, or compromising other parties (challengers) to misrepresent their location. Traditional delay-based geolocation methods focus on reducing the noise in measurements and are very vulnerable to wilful divergences from prescribed protocol. In this paper we use Internet delay measurements to securely prove the location of IP addresses while being immune to a large fraction of Byzantine actions. Our core methods are to endow Internet telemetry tools (e.g., ping) with cryptographic primitives (signatures and hash functions) together with Byzantine resistant data inferences subject to Euclidean geometric constraints. We introduce two new networking protocols, robust against Byzantine actions: Proof of Internet Geometry (PoIG) converts delay measurements into precise distance estimates across the Internet; Proof of Location (PoLoc) enables accurate and efficient multilateration of a specific IP address. The key algorithmic innovations are in conducting ``Byzantine fortified trigonometry" (BFT) inferences of data, endowing low rank matrix completion methods with Byzantine resistance.

cs.NI↗

arXiv2024

JWST observations of $^{13}$CO$_{2}$ ice: Tracing the chemical environment and thermal history of ices in protostellar envelopes

The structure and composition of simple ices can be modified during stellar evolution by protostellar heating. Key to understanding the involved processes are thermal and chemical tracers that can diagnose the history and environment of the ice. The 15.2 $μ$m bending mode of $^{12}$CO$_2$ has proven to be a valuable tracer of ice heating events but suffers from grain shape and size effects. A viable alternative tracer is the weaker $^{13}$CO$_2$ isotopologue band at 4.39 $μ$m which has now become accessible at high S/N with the $\textit{James Webb}$ Space Telescope (JWST). We present JWST NIRSpec observations of $^{13}$CO$_2$ ice in five deeply embedded Class 0 sources spanning a wide range in luminosities (0.2 - 10$^4$ L$_{\odot}$ ) taken as part of the Investigating Protostellar Accretion Across the Mass Spectrum (IPA) program. The band profiles vary significantly, with the most luminous sources showing a distinct narrow peak at 4.38 $μ$m. We first apply a phenomenological approach and show that a minimum of 3-4 Gaussian profiles are needed to fit the $^{13}$CO$_2$ absorption feature. We then combine these findings with laboratory data and show that a 15.2 $μ$m $^{12}$CO$_2$ band inspired five-component decomposition can be applied for the isotopologue band where each component is representative of CO$_2$ ice in a specific molecular environment. The final solution consists of cold mixtures of CO$_2$ with CH$_3$OH, H$_2$O and CO as well as segregated heated pure CO$_2$ ice. Our results are in agreement with previous studies of the $^{12}$CO$_2$ ice band, further confirming that $^{13}$CO$_{2}$ is a useful alternative tracer of protostellar heating events. We also propose an alternative solution consisting only of heated CO$_2$:CH$_3$OH and CO$_2$:H$_2$O ices and warm pure CO$_2$ ice for decomposing the ice profiles of the two most luminous sources in our sample.

astro-ph.GA↗

arXiv2024

A uGMRT search for radio emission from planets around evolved stars

In this work, we present the results from a study using the Giant Meterwave Radio Telescope (GMRT) to search for radio {emission} from planets around three evolved stars namely $α$~Tau, $β$~UMi, and $β$~Gem. Both $α$~Tau and $β$~UMi host massive $\sim$ 6 $M_J$ mass planets at about $\sim$1.4 au from the central star, while $β$~Gem is host to a 2.9 $M_J$ mass planet at 1.7 au from the host star. We observe $α$~Tau and $β$~ UMi at two u(upgraded)GMRT bands; band~3 (250-500~MHz) and band~4 (550-900~MHz). We also analyzed the archival observations from $β$ Gem at 150~MHz from GMRT. We did not detect any radio signals from these systems. At 400~MHz, the 3$σ$ upper limit is 87 $μ$Jy/beam for $α$~Tau~{b} and 77.4 $μ$Jy/beam for $β$~UMi~{b}. From our observations at 650~MHz, we place a 3$σ$ upper limit of 28.2 $μ$Jy/beam for $α$~Tau~b and 33.6 $μ$Jy/beam for $β$~UMi~b. For $β$ Gem b, at 150~MHz, we place an upper limit of 2.5 mJy. At 400~MHz and 650~MHz, our observations are the deepest radio images for any exoplanetary system.

astro-ph.EP↗

arXiv2024

Discovery of a collimated jet from the low luminosity protostar IRAS 16253$-$2429 in a quiescent accretion phase with the JWST

Investigating Protostellar Accretion (IPA) is a JWST Cycle~1 GO program that uses NIRSpec IFU and MIRI MRS to obtain 2.9--28~$μ$m spectral cubes of young, deeply embedded protostars with luminosities of 0.2 to 10,000~L$_{\odot}$ and central masses of 0.15 to 12~M$_{\odot}$. In this Letter, we report the discovery of a highly collimated atomic jet from the Class~0 protostar IRAS~16253$-$2429, the lowest luminosity source ($L_\mathrm{bol}$ = 0.2 $L_\odot$) in the IPA program. The collimated jet is detected in multiple [Fe~II] lines, [Ne~II], [Ni~II], and H~I lines, but not in molecular emission. The atomic jet has a velocity of about 169~$\pm$~15~km\,s$^{-1}$, after correcting for inclination. The width of the jet increases with distance from the central protostar from 23 to~60 au, corresponding to an opening angle of 2.6~$\pm$~0.5\arcdeg. By comparing the measured flux ratios of various fine structure lines to those predicted by simple shock models, we derive a shock {speed} of 54~km\,s$^{-1}$ and a preshock density of 2.0$\times10^{3}$~cm$^{-3}$ at the base of the jet. {From these quantities and using a suite of jet models and extinction laws we compute a mass loss rate between $0.4 -1.1\times10^{-10}~M_{\odot}$~yr~$^{-1}$.} The low mass loss rate is consistent with simultaneous measurements of low mass accretion rate ($2.4~\pm~0.8~\times~10^{-9}~M_{\odot}$~yr$^{-1}$) for IRAS~16253$-$2429 from JWST observations (Watson et al. in prep), indicating that the protostar is in a quiescent accretion phase. Our results demonstrate that very low-mass protostars can drive highly collimated, atomic jets, even during the quiescent phase.

astro-ph.SR↗

arXiv2023

Identifying the population of T-Tauri stars in Taurus: UV-optical synergy

With the third data release of the Gaia mission $Gaia$ DR3 with its precise photometry and astrometry, it is now possible to study the behaviour of stars at a scale never seen before. In this paper, we developed new criteria to identify T-Tauri stars (TTS) candidates using UV and optical CMDs by combining the GALEX and Gaia surveys. We found 19 TTS candidates and 5 of them are newly identified TTS in the Taurus Molecular Cloud (TMC), not catalogued before as TMC members. For some of the TTS candidates, we also obtained optical spectra from several Indian telescopes. We also present the analysis of the distance and proper motion of young stars in the Taurus using data from $Gaia$ DR3. We found that the stars in Taurus show a bimodal distribution with distance, having peaks at $130.17_{-1.24}^{1.31}$ pc and $156.25_{-5.00}^{1.86}$ pc. The reason for this bimodality, we think, is due to the fact that different clouds in the TMC region are at different distances. We further show that the two populations have similar ages and proper motion distribution. Using the $Gaia$ DR3 colour-magnitude diagram, we show that the age of Taurus is consistent with 1 Myr.

astro-ph.SR↗

arXiv2023

Optical spectroscopy of Gaia detected protostars with DOT: can we probe protostellar photospheres?

Optical spectroscopy offers the most direct view of the stellar properties and the accretion indicators. Standard accretion tracers, such as $Hβ$, $Hα$, and, Ca II triplet lines, and most photospheric features, fall in the optical wavelengths. However, these tracers are not readily observable from deeply embedded protostars because of the large line of sight extinction (Av $\sim$ 50-100 mag) toward them. In some cases, however, it is possible to observe protostars at optical wavelengths if the outflow cavity is aligned along the line-of-sight that allows observations of the photosphere, or the envelope is very tenuous and thin such that the extinction is low. In such cases, we can not only detect these protostars at optical wavelengths but also follow up spectroscopically. We have used the HOPS catalog (Furlan et al. 2016) of protostars in Orion to search for optical counterparts for protostars in the Gaia DR3 survey. Out of the 330 protostars in the HOPS sample, an optical counterpart within 2" is detected for 62 of the protostars. For 17 out of 62 optically detected protostars, we obtained optical spectra { (between 5500 to 8900 $Å$) using the Aries-Devasthal Faint Object Spectrograph \& Camera (ADFOSC) on the 3.6-m Devasthal Optical Telescope (DOT) and Hanle Faint Object Spectrograph Camera (HFOSC) on 2-m Himalayan Chandra Telescope (HCT)}. We detect strong photospheric features, such as the TiO bands in the spectra {(of 4 protostars)}, hinting that photospheres can form early on in the star formation process. We further determined the spectral types of protostars, which show photospheres similar to a late M-type. Mass accretion rates derived for the protostars are similar to those found for T-Tauri stars, in the range of 10$^{-7}$ to 10$^{-8}$ $M_\odot$/yr.

astro-ph.SR↗

arXiv2023

SAKSHI: Decentralized AI Platforms

Large AI models (e.g., Dall-E, GPT4) have electrified the scientific, technological and societal landscape through their superhuman capabilities. These services are offered largely in a traditional web2.0 format (e.g., OpenAI's GPT4 service). As more large AI models proliferate (personalizing and specializing to a variety of domains), there is a tremendous need to have a neutral trust-free platform that allows the hosting of AI models, clients receiving AI services efficiently, yet in a trust-free, incentive compatible, Byzantine behavior resistant manner. In this paper we propose SAKSHI, a trust-free decentralized platform specifically suited for AI services. The key design principles of SAKSHI are the separation of the data path (where AI query and service is managed) and the control path (where routers and compute and storage hosts are managed) from the transaction path (where the metering and billing of services are managed over a blockchain). This separation is enabled by a "proof of inference" layer which provides cryptographic resistance against a variety of misbehaviors, including poor AI service, nonpayment for service, copying of AI models. This is joint work between multiple universities (Princeton University, University of Illinois at Urbana-Champaign, Tsinghua University, HKUST) and two startup companies (Witness Chain and Eigen Layer).

cs.CR↗

arXiv2023

uGMRT observations of the hot-Saturn WASP 69b: Radio-Loud Exoplanet-Exomoon Survey II (RLEES II)

Exomoons have so far eluded ongoing searches. Several studies have exploited transit and transit timing variations and high-resolution spectroscopy to identify potential exomoon candidates. One method of detecting and confirming these exomoons is to search for signals of planet-moon interactions. In this work, we present the first radio observations of the exomoon candidate system WASP 69b. Based on the detection of alkali metals in the transmission spectra of WASP-69b, it was deduced that the system might be hosting an exomoon. WASP 69b is also one of the exoplanet systems that will be observed as part of JWST cycle-1 GTO. This makes the system an excellent target to observe and follow up. We observed the system for 32 hrs at 150 MHz and 218 MHz using the upgraded Giant Metrewave Radio Telescope (uGMRT). Though we do not detect radio emission from the systems, we place strong $3σ$ upper limits of 3.3 mJy at 150 MHz and 0.9 mJy at 218 MHz. We then use these upper limits to estimate the maximum mass loss from the exomoon candidate.

astro-ph.EP↗

arXiv2022

Continual Mean Estimation Under User-Level Privacy

We consider the problem of continually releasing an estimate of the population mean of a stream of samples that is user-level differentially private (DP). At each time instant, a user contributes a sample, and the users can arrive in arbitrary order. Until now these requirements of continual release and user-level privacy were considered in isolation. But, in practice, both these requirements come together as the users often contribute data repeatedly and multiple queries are made. We provide an algorithm that outputs a mean estimate at every time instant $t$ such that the overall release is user-level $\varepsilon$-DP and has the following error guarantee: Denoting by $M_t$ the maximum number of samples contributed by a user, as long as $\tildeΩ(1/\varepsilon)$ users have $M_t/2$ samples each, the error at time $t$ is $\tilde{O}(1/\sqrt{t}+\sqrt{M}_t/t\varepsilon)$. This is a universal error guarantee which is valid for all arrival patterns of the users. Furthermore, it (almost) matches the existing lower bounds for the single-release setting at all time instants when users have contributed equal number of samples.

cs.LG↗

arXiv2022

Unified lower bounds for interactive high-dimensional estimation under information constraints

We consider distributed parameter estimation using interactive protocols subject to local information constraints such as bandwidth limitations, local differential privacy, and restricted measurements. We provide a unified framework enabling us to derive a variety of (tight) minimax lower bounds for different parametric families of distributions, both continuous and discrete, under any $\ell_p$ loss. Our lower bound framework is versatile and yields "plug-and-play" bounds that are widely applicable to a large range of estimation problems, and, for the prototypical case of the Gaussian family, circumvents limitations of previous techniques. In particular, our approach recovers bounds obtained using data processing inequalities and Cramér--Rao bounds, two other alternative approaches for proving lower bounds in our setting of interest. Further, for the families considered, we complement our lower bounds with matching upper bounds.

cs.DS↗

arXiv2022

Wyner-Ziv Estimators for Distributed Mean Estimation with Side Information and Optimization

Communication efficient distributed mean estimation is an important primitive that arises in many distributed learning and optimization scenarios such as federated learning. Without any probabilistic assumptions on the underlying data, we study the problem of distributed mean estimation where the server has access to side information. We propose \emph{Wyner-Ziv estimators}, which are communication and computationally efficient and near-optimal when an upper bound for the distance between the side information and the data is known. As a corollary, we also show that our algorithms provide efficient schemes for the classic Wyner-Ziv problem in information theory. In a different direction, when there is no knowledge assumed about the distance between side information and the data, we present an alternative Wyner-Ziv estimator that uses correlated sampling. This latter setting offers {\em universal recovery guarantees}, and perhaps will be of interest in practice when the number of users is large and keeping track of the distances between the data and the side information may not be possible. With this mean estimator at our disposal, we revisit basic problems in decentralized optimization and compression where our Wyner-Ziv estimator yields algorithms with almost optimal performance. First, we consider the problem of communication constrained distributed optimization and provide an algorithm which attains the optimal convergence rate by exploiting the fact that the gradient estimates are close to each other. Specifically, the gradient compression scheme in our algorithm first uses half of the parties to form side information and then uses our Wyner-Ziv estimator to compress the remaining half of the gradient estimates.

cs.IT↗

arXiv2022

Proof of Backhaul: Trustfree Measurement of Broadband Bandwidth

Recent years have seen the emergence of decentralized wireless networks consisting of nodes hosted by many individuals and small enterprises, reawakening the decades-old dream of open networking. These networks have been deployed in an organic, distributed manner and are driven by new economic models resting on tokenized incentives. A critical requirement for the incentives to scale is the ability to prove network performance in a decentralized trustfree manner, i.e., a Byzantine fault tolerant network telemetry system. In this paper, we present a Proof of Backhaul (PoB) protocol which measures the bandwidth of the (broadband) backhaul link of a wireless access point, termed prover, in a decentralized and trustfree manner. In particular, our proposed protocol is the first one to satisfy the following two properties: (1) Trustfree. Bandwidth measurement is secure against Byzantine attacks by collaborations of challenge servers and the prover. (2) Open. The barrier-to-entry for being a challenge server is low; there is no requirement of having a low latency and high throughput path to the measured link. At a high-level, our protocol aggregates the challenge traffic from multiple challenge servers and uses cryptographic primitives to ensure that a subset of challengers or, even challengers and provers, cannot maliciously modify results in their favor. A formal security model allows us to establish guarantees of accurate bandwidth measurement as a function of the fraction of malicious actors. Our evaluation shows that our PoB protocol can verify backhaul bandwidth of up to 1000 Mbps with less than 8% error using measurements lasting only 100 ms. The measurement accuracy is not affected in the presence of corrupted challengers. Importantly, the basic verification protocol lends itself to a minor modification that can measure available bandwidth even in the presence of cross-traffic.

cs.CR↗

arXiv2022

The Role of Interactivity in Structured Estimation

We study high-dimensional sparse estimation under three natural constraints: communication constraints, local privacy constraints, and linear measurements (compressive sensing). Without sparsity assumptions, it has been established that interactivity cannot improve the minimax rates of estimation under these information constraints. The question of whether interactivity helps with natural inference tasks has been a topic of active research. We settle this question in the affirmative for the prototypical problems of high-dimensional sparse mean estimation and compressive sensing, by demonstrating a gap between interactive and noninteractive protocols. We further establish that the gap increases when we have more structured sparsity: for block sparsity this gap can be as large as polynomial in the dimensionality. Thus, the more structured the sparsity is, the greater is the advantage of interaction. Proving the lower bounds requires a careful breaking of a sum of correlated random variables into independent components using Baranyai's theorem on decomposition of hypergraphs, which might be of independent interest.

cs.DS↗