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Sandip Sinha - One of the best experts on this subject based on the ideXlab platform.
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beyond trace reconstruction Population Recovery from the deletion channel
Foundations of Computer Science, 2019Co-Authors: Frank Ban, Xi Chen, Adam Freilich, Rocco A. Servedio, Sandip SinhaAbstract:Population Recovery is the problem of learning an unknown distribution over an unknown set of n-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise channel. Recent work has intensively studied such problems both for the {bit-flip} noise channel and for the erasure noise channel. In this paper we initiate the study of Population Recovery under the deletion channel, in which each bit b is independently deleted with some fixed probability and the surviving bits are concatenated and transmitted. This is a far more challenging noise model than bit-flip~noise or erasure noise; indeed, even the simplest case in which the Population is of size 1 (corresponding to a trivial probability distribution supported on a single string) corresponds to the trace reconstruction problem, which is a challenging problem that has received much recent attention. In this work we give algorithms and lower bounds for Population Recovery under the deletion channel when the Population size is some value l > 1. As our main sample complexity upper bound, we show that for any Population size l = o(log n / log log n), a Population of l strings from {o,1}^n can be learned under deletion channel noise using 2^n^1/2+o(1) samples. On the lower bound side, we show that at least n^Ω (l) samples are required to perform Population Recovery under the deletion channel when the Population size is l, for all l ≤ n^1/2-e. Our upper bounds are obtained via a robust multivariate generalization of a polynomial-based analysis, due to Krasikov and Roddity [KR97], of how the k-deck of a bit-string uniquely identifies the string; this is a very different approach from recent algorithms for trace reconstruction (the l=1 case). Our lower bounds build on moment-matching results of Roos[Roos:00] and Daskalakis and Papadimitriou[DP15].
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Efficient average-case Population Recovery in the presence of insertions and deletions
arXiv: Data Structures and Algorithms, 2019Co-Authors: Frank Ban, Xi Chen, Rocco A. Servedio, Sandip SinhaAbstract:Several recent works have considered the \emph{trace reconstruction problem}, in which an unknown source string $x\in\{0,1\}^n$ is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits, resulting in a \emph{trace} of $x$. The goal is to reconstruct the original string~$x$ from independent traces of $x$. While the best algorithms known for worst-case strings use $\exp(O(n^{1/3}))$ traces \cite{DOS17,NazarovPeres17}, highly efficient algorithms are known \cite{PZ17,HPP18} for the \emph{average-case} version, in which $x$ is uniformly random. We consider a generalization of this average-case trace reconstruction problem, which we call \emph{average-case Population Recovery in the presence of insertions and deletions}. In this problem, there is an unknown distribution $\cal{D}$ over $s$ unknown source strings $x^1,\dots,x^s \in \{0,1\}^n$, and each sample is independently generated by drawing some $x^i$ from $\cal{D}$ and returning an independent trace of $x^i$. Building on \cite{PZ17} and \cite{HPP18}, we give an efficient algorithm for this problem. For any support size $s \leq \smash{\exp(\Theta(n^{1/3}))}$, for a $1-o(1)$ fraction of all $s$-element support sets $\{x^1,\dots,x^s\} \subset \{0,1\}^n$, for every distribution $\cal{D}$ supported on $\{x^1,\dots,x^s\}$, our algorithm efficiently recovers ${\cal D}$ up to total variation distance $\epsilon$ with high probability, given access to independent traces of independent draws from $\cal{D}$. The algorithm runs in time poly$(n,s,1/\epsilon)$ and its sample complexity is poly$(s,1/\epsilon,\exp(\log^{1/3}n)).$ This polynomial dependence on the support size $s$ is in sharp contrast with the \emph{worst-case} version (when $x^1,\dots,x^s$ may be any strings in $\{0,1\}^n$), in which the sample complexity of the most efficient known algorithm \cite{BCFSS19} is doubly exponential in $s$.
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Beyond trace reconstruction: Population Recovery from the deletion channel
arXiv: Data Structures and Algorithms, 2019Co-Authors: Frank Ban, Xi Chen, Adam Freilich, Rocco A. Servedio, Sandip SinhaAbstract:\emph{Population Recovery} is the problem of learning an unknown distribution over an unknown set of $n$-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise channel. Recent work has intensively studied such problems both for the bit-flip and erasure noise channels. We initiate the study of Population Recovery under the \emph{deletion channel}, in which each bit is independently \emph{deleted} with some fixed probability and the surviving bits are concatenated and transmitted. This is a far more challenging noise model than bit-flip~noise or erasure noise; indeed, even the simplest case in which the Population size is 1 (corresponding to a trivial distribution supported on a single string) corresponds to the \emph{trace reconstruction} problem, a challenging problem that has received much recent attention (see e.g.~\cite{DOS17,NP17,PZ17,HPP18,HHP18}). We give algorithms and lower bounds for Population Recovery under the deletion channel when the Population size is some $\ell>1$. As our main sample complexity upper bound, we show that for any $\ell=o(\log n/\log \log n)$, a Population of $\ell$ strings from $\{0,1\}^n$ can be learned under deletion channel noise using $\smash{2^{n^{1/2+o(1)}}}$ samples. On the lower bound side, we show that $n^{\Omega(\ell)}$ samples are required to perform Population Recovery under the deletion channel, for all $\ell \leq n^{1/2-\epsilon}$. Our upper bounds are obtained via a robust multivariate generalization of a polynomial-based analysis, due to Krasikov and Roddity \cite{KR97}, of how the $k$-deck of a bit-string uniquely identifies the string; this is a very different approach from recent algorithms for trace reconstruction (the $\ell=1$ case). Our lower bounds build on moment-matching results of Roos~\cite{Roo00} and Daskalakis and Papadimitriou~\cite{DP15}.
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FOCS - Beyond Trace Reconstruction: Population Recovery from the Deletion Channel
2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019Co-Authors: Frank Ban, Xi Chen, Adam Freilich, Rocco A. Servedio, Sandip SinhaAbstract:Population Recovery is the problem of learning an unknown distribution over an unknown set of n-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise channel. Recent work has intensively studied such problems both for the {bit-flip} noise channel and for the erasure noise channel. In this paper we initiate the study of Population Recovery under the deletion channel, in which each bit b is independently deleted with some fixed probability and the surviving bits are concatenated and transmitted. This is a far more challenging noise model than bit-flip~noise or erasure noise; indeed, even the simplest case in which the Population is of size 1 (corresponding to a trivial probability distribution supported on a single string) corresponds to the trace reconstruction problem, which is a challenging problem that has received much recent attention. In this work we give algorithms and lower bounds for Population Recovery under the deletion channel when the Population size is some value l > 1. As our main sample complexity upper bound, we show that for any Population size l = o(log n / log log n), a Population of l strings from {o,1}^n can be learned under deletion channel noise using 2^n^1/2+o(1) samples. On the lower bound side, we show that at least n^Ω (l) samples are required to perform Population Recovery under the deletion channel when the Population size is l, for all l ≤ n^1/2-e. Our upper bounds are obtained via a robust multivariate generalization of a polynomial-based analysis, due to Krasikov and Roddity [KR97], of how the k-deck of a bit-string uniquely identifies the string; this is a very different approach from recent algorithms for trace reconstruction (the l=1 case). Our lower bounds build on moment-matching results of Roos[Roos:00] and Daskalakis and Papadimitriou[DP15].
Jiapeng Zhang - One of the best experts on this subject based on the ideXlab platform.
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improved noisy Population Recovery and reverse bonami beckner inequality for sparse functions
Symposium on the Theory of Computing, 2015Co-Authors: Shachar Lovett, Jiapeng ZhangAbstract:The noisy Population Recovery problem is a basic statistical inference problem. Given an unknown distribution in {0,1}n with support of size k, and given access only to noisy samples from it, where each bit is flipped independently with probability (1-μ)/2, estimate the original probability up to an additive error of e. We give an algorithm which solves this problem in time polynomial in (klog log k, n, 1/e). This improves on the previous algorithm of Wigderson and Yehudayoff [FOCS 2012] which solves the problem in time polynomial in (klog k, n, 1/e). Our main technical contribution, which facilitates the algorithm, is a new reverse Bonami-Beckner inequality for the L1 norm of sparse functions.
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STOC - Improved Noisy Population Recovery, and Reverse Bonami-Beckner Inequality for Sparse Functions
Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15, 2015Co-Authors: Shachar Lovett, Jiapeng ZhangAbstract:The noisy Population Recovery problem is a basic statistical inference problem. Given an unknown distribution in {0,1}n with support of size k, and given access only to noisy samples from it, where each bit is flipped independently with probability (1-μ)/2, estimate the original probability up to an additive error of e. We give an algorithm which solves this problem in time polynomial in (klog log k, n, 1/e). This improves on the previous algorithm of Wigderson and Yehudayoff [FOCS 2012] which solves the problem in time polynomial in (klog k, n, 1/e). Our main technical contribution, which facilitates the algorithm, is a new reverse Bonami-Beckner inequality for the L1 norm of sparse functions.
Daniel Esler - One of the best experts on this subject based on the ideXlab platform.
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Timelines and mechanisms of wildlife Population Recovery following the Exxon Valdez Oil Spill
Deep Sea Research Part II: Topical Studies in Oceanography, 2018Co-Authors: Daniel Esler, Brenda E. Ballachey, Craig O. Matkin, Daniel A. Cushing, Robert Kaler, James L. Bodkin, Daniel H. Monson, George G. Esslinger, Kimberly A. KloeckerAbstract:Abstract Research and monitoring activities over the 28 years since the T/V Exxon Valdez ran aground and spilled oil into Prince William Sound, Alaska have led to an improved understanding of how wildlife Populations were damaged, as well as the mechanisms and timelines of Recovery. A key finding was that for some species, such as harlequin ducks and sea otters, chronic oil spill effects persisted for at least two decades and were a larger influence on Population dynamics over the long term than acute effects of the spill. These data also offer insights into Population variation resulting from factors other than the oil spill. For example, while many seabirds experienced direct and indirect effects of the spill, Population trajectories of some piscivorous birds, including pigeon guillemots and marbled murrelets, were linked to long-term environmental changes independent of spill effects. Another species, killer whales, suffered Population declines due to acute spill effects that have not been resolved despite lack of chronic direct effects, representing a novel pathway of long-term injury. The observed variation in mechanisms and timelines of Recovery is linked to species specific life history and natural history traits, and thus may be useful for predicting Population Recovery for other species following other spills.
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Harlequin duck Population Recovery following the 'Exxon Valdez' oil spill: progress, process and constraints
Marine Ecology Progress Series, 2002Co-Authors: Daniel Esler, Timothy D. Bowman, Kimberly A. Trust, Brenda E. Ballachey, Thomas A. Dean, Stephen C. Jewett, Charles E. O'clairAbstract:Following the 1989 'Exxon Valdez' oil spill in Prince William Sound, Alaska, we studied the status of Recovery of harlequin duck Histrionicus histrionicus Populations during 1995 to 1998. We evaluated potential constraints on full Recovery, including (1) exposure to residual oil; (2) food limita- tion; and (3) intrinsic demographic limitations on Population growth rates. In this paper, we synthe- size the findings from our work and incorporate information from other harlequin duck research and monitoring programs to provide a comprehensive evaluation of the response of this species to the 'Exxon Valdez' spill. We conclude that harlequin duck Populations had not fully recovered by 1998. Furthermore, adverse effects continued as many as 9 yr after the oil spill, in contrast to the conven- tional paradigm that oil spill effects on bird Populations are short-lived. These conclusions are based on the findings that (1) elevated cytochrome P450 (CYP1A) induction on oiled areas indicated con- tinued exposure to oil in 1998; (2) adult female winter survival was lower on oiled than unoiled areas during 1995 to 1998; (3) fall Population surveys by the Alaska Department of Fish and Game indi- cated numerical declines in oiled areas during 1995 to 1997; and (4) densities on oiled areas in 1996 and 1997 were lower than expected using models that accounted for effects of habitat attributes. Based on hypothesized links between oil contamination and demography, we suggest that harlequin duck Population Recovery was constrained primarily by continued oil exposure. Full Population Recovery will also be delayed by the time necessary for intrinsic Population growth to allow return to pre-spill numbers following cessation of residual oil spill effects. Although not all wildlife species were affected by the 'Exxon Valdez' oil spill, and some others may have recovered quickly from any effects, harlequin duck life history characteristics and benthic, nearshore feeding habits make them susceptible to both initial and long-term oil spill effects.
Frank Ban - One of the best experts on this subject based on the ideXlab platform.
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beyond trace reconstruction Population Recovery from the deletion channel
Foundations of Computer Science, 2019Co-Authors: Frank Ban, Xi Chen, Adam Freilich, Rocco A. Servedio, Sandip SinhaAbstract:Population Recovery is the problem of learning an unknown distribution over an unknown set of n-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise channel. Recent work has intensively studied such problems both for the {bit-flip} noise channel and for the erasure noise channel. In this paper we initiate the study of Population Recovery under the deletion channel, in which each bit b is independently deleted with some fixed probability and the surviving bits are concatenated and transmitted. This is a far more challenging noise model than bit-flip~noise or erasure noise; indeed, even the simplest case in which the Population is of size 1 (corresponding to a trivial probability distribution supported on a single string) corresponds to the trace reconstruction problem, which is a challenging problem that has received much recent attention. In this work we give algorithms and lower bounds for Population Recovery under the deletion channel when the Population size is some value l > 1. As our main sample complexity upper bound, we show that for any Population size l = o(log n / log log n), a Population of l strings from {o,1}^n can be learned under deletion channel noise using 2^n^1/2+o(1) samples. On the lower bound side, we show that at least n^Ω (l) samples are required to perform Population Recovery under the deletion channel when the Population size is l, for all l ≤ n^1/2-e. Our upper bounds are obtained via a robust multivariate generalization of a polynomial-based analysis, due to Krasikov and Roddity [KR97], of how the k-deck of a bit-string uniquely identifies the string; this is a very different approach from recent algorithms for trace reconstruction (the l=1 case). Our lower bounds build on moment-matching results of Roos[Roos:00] and Daskalakis and Papadimitriou[DP15].
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Efficient average-case Population Recovery in the presence of insertions and deletions
arXiv: Data Structures and Algorithms, 2019Co-Authors: Frank Ban, Xi Chen, Rocco A. Servedio, Sandip SinhaAbstract:Several recent works have considered the \emph{trace reconstruction problem}, in which an unknown source string $x\in\{0,1\}^n$ is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits, resulting in a \emph{trace} of $x$. The goal is to reconstruct the original string~$x$ from independent traces of $x$. While the best algorithms known for worst-case strings use $\exp(O(n^{1/3}))$ traces \cite{DOS17,NazarovPeres17}, highly efficient algorithms are known \cite{PZ17,HPP18} for the \emph{average-case} version, in which $x$ is uniformly random. We consider a generalization of this average-case trace reconstruction problem, which we call \emph{average-case Population Recovery in the presence of insertions and deletions}. In this problem, there is an unknown distribution $\cal{D}$ over $s$ unknown source strings $x^1,\dots,x^s \in \{0,1\}^n$, and each sample is independently generated by drawing some $x^i$ from $\cal{D}$ and returning an independent trace of $x^i$. Building on \cite{PZ17} and \cite{HPP18}, we give an efficient algorithm for this problem. For any support size $s \leq \smash{\exp(\Theta(n^{1/3}))}$, for a $1-o(1)$ fraction of all $s$-element support sets $\{x^1,\dots,x^s\} \subset \{0,1\}^n$, for every distribution $\cal{D}$ supported on $\{x^1,\dots,x^s\}$, our algorithm efficiently recovers ${\cal D}$ up to total variation distance $\epsilon$ with high probability, given access to independent traces of independent draws from $\cal{D}$. The algorithm runs in time poly$(n,s,1/\epsilon)$ and its sample complexity is poly$(s,1/\epsilon,\exp(\log^{1/3}n)).$ This polynomial dependence on the support size $s$ is in sharp contrast with the \emph{worst-case} version (when $x^1,\dots,x^s$ may be any strings in $\{0,1\}^n$), in which the sample complexity of the most efficient known algorithm \cite{BCFSS19} is doubly exponential in $s$.
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Beyond trace reconstruction: Population Recovery from the deletion channel
arXiv: Data Structures and Algorithms, 2019Co-Authors: Frank Ban, Xi Chen, Adam Freilich, Rocco A. Servedio, Sandip SinhaAbstract:\emph{Population Recovery} is the problem of learning an unknown distribution over an unknown set of $n$-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise channel. Recent work has intensively studied such problems both for the bit-flip and erasure noise channels. We initiate the study of Population Recovery under the \emph{deletion channel}, in which each bit is independently \emph{deleted} with some fixed probability and the surviving bits are concatenated and transmitted. This is a far more challenging noise model than bit-flip~noise or erasure noise; indeed, even the simplest case in which the Population size is 1 (corresponding to a trivial distribution supported on a single string) corresponds to the \emph{trace reconstruction} problem, a challenging problem that has received much recent attention (see e.g.~\cite{DOS17,NP17,PZ17,HPP18,HHP18}). We give algorithms and lower bounds for Population Recovery under the deletion channel when the Population size is some $\ell>1$. As our main sample complexity upper bound, we show that for any $\ell=o(\log n/\log \log n)$, a Population of $\ell$ strings from $\{0,1\}^n$ can be learned under deletion channel noise using $\smash{2^{n^{1/2+o(1)}}}$ samples. On the lower bound side, we show that $n^{\Omega(\ell)}$ samples are required to perform Population Recovery under the deletion channel, for all $\ell \leq n^{1/2-\epsilon}$. Our upper bounds are obtained via a robust multivariate generalization of a polynomial-based analysis, due to Krasikov and Roddity \cite{KR97}, of how the $k$-deck of a bit-string uniquely identifies the string; this is a very different approach from recent algorithms for trace reconstruction (the $\ell=1$ case). Our lower bounds build on moment-matching results of Roos~\cite{Roo00} and Daskalakis and Papadimitriou~\cite{DP15}.
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FOCS - Beyond Trace Reconstruction: Population Recovery from the Deletion Channel
2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019Co-Authors: Frank Ban, Xi Chen, Adam Freilich, Rocco A. Servedio, Sandip SinhaAbstract:Population Recovery is the problem of learning an unknown distribution over an unknown set of n-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise channel. Recent work has intensively studied such problems both for the {bit-flip} noise channel and for the erasure noise channel. In this paper we initiate the study of Population Recovery under the deletion channel, in which each bit b is independently deleted with some fixed probability and the surviving bits are concatenated and transmitted. This is a far more challenging noise model than bit-flip~noise or erasure noise; indeed, even the simplest case in which the Population is of size 1 (corresponding to a trivial probability distribution supported on a single string) corresponds to the trace reconstruction problem, which is a challenging problem that has received much recent attention. In this work we give algorithms and lower bounds for Population Recovery under the deletion channel when the Population size is some value l > 1. As our main sample complexity upper bound, we show that for any Population size l = o(log n / log log n), a Population of l strings from {o,1}^n can be learned under deletion channel noise using 2^n^1/2+o(1) samples. On the lower bound side, we show that at least n^Ω (l) samples are required to perform Population Recovery under the deletion channel when the Population size is l, for all l ≤ n^1/2-e. Our upper bounds are obtained via a robust multivariate generalization of a polynomial-based analysis, due to Krasikov and Roddity [KR97], of how the k-deck of a bit-string uniquely identifies the string; this is a very different approach from recent algorithms for trace reconstruction (the l=1 case). Our lower bounds build on moment-matching results of Roos[Roos:00] and Daskalakis and Papadimitriou[DP15].
Brenda E. Ballachey - One of the best experts on this subject based on the ideXlab platform.
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Timelines and mechanisms of wildlife Population Recovery following the Exxon Valdez Oil Spill
Deep Sea Research Part II: Topical Studies in Oceanography, 2018Co-Authors: Daniel Esler, Brenda E. Ballachey, Craig O. Matkin, Daniel A. Cushing, Robert Kaler, James L. Bodkin, Daniel H. Monson, George G. Esslinger, Kimberly A. KloeckerAbstract:Abstract Research and monitoring activities over the 28 years since the T/V Exxon Valdez ran aground and spilled oil into Prince William Sound, Alaska have led to an improved understanding of how wildlife Populations were damaged, as well as the mechanisms and timelines of Recovery. A key finding was that for some species, such as harlequin ducks and sea otters, chronic oil spill effects persisted for at least two decades and were a larger influence on Population dynamics over the long term than acute effects of the spill. These data also offer insights into Population variation resulting from factors other than the oil spill. For example, while many seabirds experienced direct and indirect effects of the spill, Population trajectories of some piscivorous birds, including pigeon guillemots and marbled murrelets, were linked to long-term environmental changes independent of spill effects. Another species, killer whales, suffered Population declines due to acute spill effects that have not been resolved despite lack of chronic direct effects, representing a novel pathway of long-term injury. The observed variation in mechanisms and timelines of Recovery is linked to species specific life history and natural history traits, and thus may be useful for predicting Population Recovery for other species following other spills.
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Harlequin duck Population Recovery following the 'Exxon Valdez' oil spill: progress, process and constraints
Marine Ecology Progress Series, 2002Co-Authors: Daniel Esler, Timothy D. Bowman, Kimberly A. Trust, Brenda E. Ballachey, Thomas A. Dean, Stephen C. Jewett, Charles E. O'clairAbstract:Following the 1989 'Exxon Valdez' oil spill in Prince William Sound, Alaska, we studied the status of Recovery of harlequin duck Histrionicus histrionicus Populations during 1995 to 1998. We evaluated potential constraints on full Recovery, including (1) exposure to residual oil; (2) food limita- tion; and (3) intrinsic demographic limitations on Population growth rates. In this paper, we synthe- size the findings from our work and incorporate information from other harlequin duck research and monitoring programs to provide a comprehensive evaluation of the response of this species to the 'Exxon Valdez' spill. We conclude that harlequin duck Populations had not fully recovered by 1998. Furthermore, adverse effects continued as many as 9 yr after the oil spill, in contrast to the conven- tional paradigm that oil spill effects on bird Populations are short-lived. These conclusions are based on the findings that (1) elevated cytochrome P450 (CYP1A) induction on oiled areas indicated con- tinued exposure to oil in 1998; (2) adult female winter survival was lower on oiled than unoiled areas during 1995 to 1998; (3) fall Population surveys by the Alaska Department of Fish and Game indi- cated numerical declines in oiled areas during 1995 to 1997; and (4) densities on oiled areas in 1996 and 1997 were lower than expected using models that accounted for effects of habitat attributes. Based on hypothesized links between oil contamination and demography, we suggest that harlequin duck Population Recovery was constrained primarily by continued oil exposure. Full Population Recovery will also be delayed by the time necessary for intrinsic Population growth to allow return to pre-spill numbers following cessation of residual oil spill effects. Although not all wildlife species were affected by the 'Exxon Valdez' oil spill, and some others may have recovered quickly from any effects, harlequin duck life history characteristics and benthic, nearshore feeding habits make them susceptible to both initial and long-term oil spill effects.