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diff --git a/poster/Finale_poster/beamerthemeconfposter.sty b/poster/Finale_poster/beamerthemeconfposter.sty index fc07a08..44acd17 100644 --- a/poster/Finale_poster/beamerthemeconfposter.sty +++ b/poster/Finale_poster/beamerthemeconfposter.sty @@ -99,12 +99,14 @@ \begin{column}{.6\linewidth} \vskip1cm \centering - \usebeamercolor{title in headline}{\color{jblue}\Huge{\textbf{\inserttitle}}\\[0.5ex]} - \usebeamercolor{author in headline}{\color{fg}\Large{\insertauthor}\\[1ex]} + \usebeamercolor{title in headline}{\color{jblue}\huge{\textbf{\inserttitle}}\\[0.5ex]} %\usebeamercolor{institute in headline}{\color{fg}\large{\insertinstitute}\\[1ex]} \end{column} \vspace{1cm} \begin{column}{.2\linewidth} + \begin{center} + \usebeamercolor{author in headline}{\color{fg}\Large{\insertauthor}\\[1ex]} +\end{center} \end{column} \vspace{1cm} \end{columns} diff --git a/poster/Finale_poster/fig.png b/poster/Finale_poster/fig.png Binary files differnew file mode 100644 index 0000000..4d594d4 --- /dev/null +++ b/poster/Finale_poster/fig.png diff --git a/poster/Finale_poster/poster.tex b/poster/Finale_poster/poster.tex index 1365801..7865e18 100644 --- a/poster/Finale_poster/poster.tex +++ b/poster/Finale_poster/poster.tex @@ -1,6 +1,6 @@ \documentclass[final]{beamer} \usepackage[utf8]{inputenc} -\usepackage[scale=1.8]{beamerposter} % Use the beamerposter package for laying +\usepackage[scale=1.7]{beamerposter} % Use the beamerposter package for laying \usetheme{confposter} % Use the confposter theme supplied with this template \usepackage{framed, amsmath, amsthm, amssymb} \usepackage{graphicx} @@ -16,7 +16,7 @@ \newlength{\twocolwid} \newlength{\threecolwid} \setlength{\paperwidth}{48in} % A0 width: 46.8in -\setlength{\paperheight}{40in} % A0 height: 33.1in +\setlength{\paperheight}{36in} % A0 height: 33.1in \setlength{\sepwid}{0.024\paperwidth} % Separation width (white space) between \setlength{\onecolwid}{0.29\paperwidth} % Width of one column \setlength{\twocolwid}{0.464\paperwidth} % Width of two columns @@ -24,7 +24,7 @@ \setlength{\topmargin}{-1in} % Reduce the top margin size \title{Bayesian and Active Learning for Graph Inference} % Poster title -\author{Thibaut Horel\and Jean Pouget-Abadie} % Author(s) +\author{Thibaut Horel\\[0.5em] Jean Pouget-Abadie} % Author(s) \begin{document} \setlength{\belowcaptionskip}{2ex} % White space under figures @@ -44,9 +44,9 @@ \item \textbf{Objective:} learn $\Theta$, matrix of edge weights. \end{itemize} \end{block} -\vspace{1cm} +\vspace{2cm} -\begin{block}{\bf Contagion Model~\cite{}} +\begin{block}{\bf Contagion Model~\cite{Pouget:2015}} \begin{itemize} \item $X^t\in\{0,1\}^N$: state of the network at time $t$ \item At $t=0$, $X^0$ drawn from \emph{source distribution} @@ -67,6 +67,7 @@ \end{center} \end{figure} \end{block} +\vspace{2cm} \begin{block}{MLE} \begin{itemize} @@ -81,7 +82,7 @@ Can be solved efficiently by SGD on $\Theta$. \vspace{1cm} \item log-likelihood is concave for common contagion models (\emph{e.g} IC - model) $\Rightarrow$ provable convergence guarantees (\cite{}). + model) $\Rightarrow$ provable convergence guarantees \cite{Netrapalli:2012}. \end{itemize} \end{block} \end{column} % End of the first column @@ -94,6 +95,7 @@ \begin{block}{Bayesian Framework} \begin{figure} \centering + \vspace{-1em} \includegraphics[scale=3]{graphical.pdf} \end{figure} {\bf Advantages:} @@ -113,23 +115,27 @@ \begin{center}--~OR~--\end{center} \emph{Can we cherry-pick the most relevant part of the dataset?} +\vspace{0.5em} {\bf Idea:} Focus on parts of the graph which are unexplored (high uncertainty). -i.e.~maximize information gain per cascade +i.e.~maximize information gain per observation. -Baseline heuristic: +\vspace{0.5em} +\textbf{Baseline heuristic:} \begin{itemize} - \item Choose source proportional to estimated out-degree $\implies$ wider + \item Choose source w.p. proportional to estimated out-degree $\implies$ wider cascades $\implies$ more data \end{itemize} -Principled heuristic: +\vspace{0.5em} +\textbf{Principled heuristic:} \begin{itemize} - \item Choose source proportional to mutual information - \begin{equation*} - I((X_t) ,\Theta | x^0 = i) = - H(\Theta | (X_t), X_0 = i) + H(\Theta) - \end{equation*} - \item Exact strategy requires knowing true distribution of $(X_t)$ - \item Use estimated $\Theta$ to compute $H(\Theta | (X_t), X_0 = i)$ + \item Choose source w.p. proportional to mutual information + \begin{multline*} + p(i) \propto I\big(\{X_t\}_{t\geq 1} ,\Theta | X^0 = \{i\}\big)\\ + = H(\Theta) - H\big(\Theta | \{X_t\}_{t\geq 1}, X_0 = \{i\}\big) + \end{multline*} +\item Requires knowing true distribution of $\{X_t\}$ $\Rightarrow$ use current + estimate of $\Theta$ instead. \end{itemize} \end{block} \end{column} @@ -142,34 +148,42 @@ Principled heuristic: \begin{block}{Implementation} {\bf Scalable Bayesian Inference} \begin{itemize} - \item MCMC (PyMC~\cite{}) - \item VI (BLOCKS~\cite{}) + \item MCMC: implements the graphical model directly with PyMC + \cite{pymc}; does not scale beyond 10 nodes. + \item VI: implements variational inference with Blocks~\cite{blocks}. + (wip: use Bohning bounds to avoid sampling). \end{itemize} - {\bf Scalable Active Learning Criterion} -Approx.~heuristic: + \vspace{1em} + {\bf Scalable Active Learning} + + Mutual information is expensive to compute. Instead: \begin{itemize} - \item Choose source proportional to mutual information of first step of - cascade and $\Theta$: Hope for closed-form formula - \item Intuition: - \begin{itemize} - \item Choose lower bound of mutual information $I(X, Y) \geq I(f(X), - g(Y))$ where $f$ is the trunctation function - \item First step is most informative~\cite{} - \end{itemize} - \item Sum over outgoing-edges' variance as proxy + \item use mutual information between $\Theta$ and $X^1$. + + \textbf{Justification} for any $f$: + \begin{displaymath} + I(X, Y) \geq I\big(f(X)\big) + \end{displaymath} + in our case: $f$ truncates the cascade at $t=1$. + + (wip: obtain closed-form formula in this case). + \item variance is a lower-bound on mutual information $\implies$ pick + node $i$ w.p. proportional to $\sum_j \text{Var}(\Theta_{i,j})$. \end{itemize} \end{block} \begin{block}{Results} - + \begin{center} + \includegraphics[scale=1.5]{fig.png} + \end{center} \end{block} \begin{block}{References} - {\scriptsize \bibliography{../../paper/sparse} -\bibliographystyle{plain}} + {\scriptsize \bibliography{sparse} +\bibliographystyle{abbrv}} \end{block} %----------------------------------------------------------------------------- diff --git a/poster/Finale_poster/sparse.bib b/poster/Finale_poster/sparse.bib new file mode 100644 index 0000000..61d57fa --- /dev/null +++ b/poster/Finale_poster/sparse.bib @@ -0,0 +1,541 @@ +@article{pymc, + title={PyMC: Bayesian stochastic modelling in Python}, + author={Patil, Anand and Huard, David and Fonnesbeck, Christopher J}, + journal={Journal of statistical software}, + volume={35}, + number={4}, + pages={1}, + year={2010}, + publisher={Europe PMC Funders} +} + +@article{blocks, + author = {Bart van Merri{\"{e}}nboer and + Dzmitry Bahdanau and + Vincent Dumoulin and + Dmitriy Serdyuk and + David Warde{-}Farley and + Jan Chorowski and + Yoshua Bengio}, + title = {Blocks and Fuel: Frameworks for deep learning}, + journal = {CoRR}, + volume = {abs/1506.00619}, + year = {2015}, + url = {http://arxiv.org/abs/1506.00619}, + timestamp = {Wed, 01 Jul 2015 15:10:24 +0200}, + biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/MerrienboerBDSW15}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article {CandesRomberTao:2006, +author = {Candès, Emmanuel J. and Romberg, Justin K. and Tao, Terence}, +title = {Stable signal recovery from incomplete and inaccurate measurements}, +journal = {Communications on Pure and Applied Mathematics}, +volume = {59}, +number = {8}, +publisher = {Wiley Subscription Services, Inc., A Wiley Company}, +issn = {1097-0312}, +pages = {1207--1223}, +year = {2006}, +} + + +@inproceedings{GomezRodriguez:2010, + author = {Gomez Rodriguez, Manuel and Leskovec, Jure and Krause, Andreas}, + title = {Inferring Networks of Diffusion and Influence}, + booktitle = {Proceedings of the 16th ACM SIGKDD International Conference on + Knowledge Discovery and Data Mining}, + series = {KDD '10}, + year = {2010}, + isbn = {978-1-4503-0055-1}, + location = {Washington, DC, USA}, + pages = {1019--1028}, + numpages = {10}, + publisher = {ACM}, + address = {New York, NY, USA}, +} + +@inproceedings{Pouget:2015, + title={Inferring graphs from cascades: A Sparse Recovery Framework}, + author={Pouget-Abadie, Jean and Horel, Thibaut}, + series={ICML'15}, + year={2015} +} + +@inproceedings{du2013uncover, + title={Uncover topic-sensitive information diffusion networks}, + author={Du, Nan and Song, Le and Woo, Hyenkyun and Zha, Hongyuan}, + booktitle={Proceedings of the Sixteenth International Conference on + Artificial Intelligence and Statistics}, + pages={229--237}, + year={2013} +} + +@inproceedings{du2014influence, + title={Influence function learning in information diffusion networks}, + author={Du, Nan and Liang, Yingyu and Balcan, Maria and Song, Le}, + booktitle={Proceedings of the 31st International Conference on Machine + Learning (ICML-14)}, + pages={2016--2024}, + year={2014} +} + + +@article{Netrapalli:2012, + author = {Netrapalli, Praneeth and Sanghavi, Sujay}, + title = {Learning the Graph of Epidemic Cascades}, + journal = {SIGMETRICS Perform. Eval. Rev.}, + volume = {40}, + number = {1}, + month = {June}, + year = {2012}, + issn = {0163-5999}, + numpages = {12}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {cascades, epidemics, graph structure learning}, +} + +@article{Negahban:2009, + author = {Negahban, Sahand N. and Ravikumar, Pradeep and Wrainwright, Martin J. and Yu, Bin}, + title = {A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers}, + Journal = {Statistical Science}, + year = {2012}, + month = {December}, + volume = {27}, + number = {4}, + pages = {538--557}, +} + +@article{Zhao:2006, + author = {Zhao, Peng and Yu, Bin}, + title = {On Model Selection Consistency of Lasso}, + journal = {J. Mach. Learn. Res.}, + issue_date = {12/1/2006}, + volume = {7}, + month = dec, + year = {2006}, + issn = {1532-4435}, + pages = {2541--2563}, + numpages = {23}, + acmid = {1248637}, + publisher = {JMLR.org}, +} + +@inproceedings{Daneshmand:2014, + author = {Hadi Daneshmand and + Manuel Gomez{-}Rodriguez and + Le Song and + Bernhard Sch{\"{o}}lkopf}, + title = {Estimating Diffusion Network Structures: Recovery Conditions, Sample + Complexity {\&} Soft-thresholding Algorithm}, + booktitle = {Proceedings of the 31th International Conference on Machine Learning, + {ICML} 2014, Beijing, China, 21-26 June 2014}, + pages = {793--801}, + year = {2014}, + timestamp = {Fri, 07 Nov 2014 20:42:30 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@inproceedings{Kempe:03, + author = {David Kempe and + Jon M. Kleinberg and + {\'{E}}va Tardos}, + title = {Maximizing the spread of influence through a social network}, + booktitle = {Proceedings of the Ninth {ACM} {SIGKDD} International Conference on + Knowledge Discovery and Data Mining, Washington, DC, USA, August 24 + - 27, 2003}, + pages = {137--146}, + year = {2003}, + timestamp = {Mon, 13 Feb 2006 15:34:20 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@inproceedings{Abrahao:13, + author = {Bruno D. Abrahao and + Flavio Chierichetti and + Robert Kleinberg and + Alessandro Panconesi}, + title = {Trace complexity of network inference}, + booktitle = {The 19th {ACM} {SIGKDD} International Conference on Knowledge Discovery + and Data Mining, {KDD} 2013, Chicago, IL, USA, August 11-14, 2013}, + pages = {491--499}, + year = {2013}, + timestamp = {Tue, 10 Sep 2013 10:11:57 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + + +@article{vandegeer:2009, +author = "van de Geer, Sara A. and B{\"u}hlmann, Peter", +fjournal = "Electronic Journal of Statistics", +journal = "Electron. J. Statist.", +pages = "1360--1392", +publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", +title = "On the conditions used to prove oracle results for the Lasso", +volume = "3", +year = "2009" +} + +@article{vandegeer:2011, +author = "van de Geer, Sara and Bühlmann, Peter and Zhou, Shuheng", +fjournal = "Electronic Journal of Statistics", +journal = "Electron. J. Statist.", +pages = "688--749", +publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", +title = "The adaptive and the thresholded Lasso for potentially misspecified + models (and a lower bound for the Lasso)", +volume = "5", +year = "2011" +} + +@article{Zou:2006, +author = {Zou, Hui}, +title = {The Adaptive Lasso and Its Oracle Properties}, +journal = {Journal of the American Statistical Association}, +volume = {101}, +number = {476}, +pages = {1418-1429}, +year = {2006}, +} + +@article{Jacques:2013, + author = {Laurent Jacques and + Jason N. Laska and + Petros T. Boufounos and + Richard G. Baraniuk}, + title = {Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of + Sparse Vectors}, + journal = {{IEEE} Transactions on Information Theory}, + volume = {59}, + number = {4}, + pages = {2082--2102}, + year = {2013}, + timestamp = {Tue, 09 Apr 2013 19:57:48 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@inproceedings{Boufounos:2008, + author = {Petros Boufounos and + Richard G. Baraniuk}, + title = {1-Bit compressive sensing}, + booktitle = {42nd Annual Conference on Information Sciences and Systems, {CISS} + 2008, Princeton, NJ, USA, 19-21 March 2008}, + pages = {16--21}, + year = {2008}, + timestamp = {Wed, 15 Oct 2014 17:04:27 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@inproceedings{Gupta:2010, + author = {Ankit Gupta and + Robert Nowak and + Benjamin Recht}, + title = {Sample complexity for 1-bit compressed sensing and sparse + classification}, + booktitle = {{IEEE} International Symposium on Information Theory, {ISIT} 2010, + June 13-18, 2010, Austin, Texas, USA, Proceedings}, + pages = {1553--1557}, + year = {2010}, + timestamp = {Thu, 15 Jan 2015 17:11:50 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{Plan:2014, + author = {Yaniv Plan and + Roman Vershynin}, + title = {Dimension Reduction by Random Hyperplane Tessellations}, + journal = {Discrete {\&} Computational Geometry}, + volume = {51}, + number = {2}, + pages = {438--461}, + year = {2014}, + timestamp = {Tue, 11 Feb 2014 13:48:56 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{bickel:2009, +author = "Bickel, Peter J. and Ritov, Ya’acov and Tsybakov, Alexandre B.", +fjournal = "The Annals of Statistics", +journal = "Ann. Statist.", +month = "08", +number = "4", +pages = "1705--1732", +publisher = "The Institute of Mathematical Statistics", +title = "Simultaneous analysis of Lasso and Dantzig selector", +volume = "37", +year = "2009" +} + +@article{raskutti:10, + author = {Garvesh Raskutti and + Martin J. Wainwright and + Bin Yu}, + title = {Restricted Eigenvalue Properties for Correlated Gaussian Designs}, + journal = {Journal of Machine Learning Research}, + volume = {11}, + pages = {2241--2259}, + year = {2010}, + timestamp = {Wed, 15 Oct 2014 17:04:32 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{rudelson:13, + author = {Mark Rudelson and + Shuheng Zhou}, + title = {Reconstruction From Anisotropic Random Measurements}, + journal = {{IEEE} Transactions on Information Theory}, + volume = {59}, + number = {6}, + pages = {3434--3447}, + year = {2013}, + timestamp = {Tue, 21 May 2013 14:15:50 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{bipw11, + author = {Khanh Do Ba and + Piotr Indyk and + Eric Price and + David P. Woodruff}, + title = {Lower Bounds for Sparse Recovery}, + journal = {CoRR}, + volume = {abs/1106.0365}, + year = {2011}, + timestamp = {Mon, 05 Dec 2011 18:04:39 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@inproceedings{pw11, + author = {Eric Price and + David P. Woodruff}, + title = {{(1} + eps)-Approximate Sparse Recovery}, + booktitle = {{IEEE} 52nd Annual Symposium on Foundations of Computer Science, + {FOCS} 2011, Palm Springs, CA, USA, October 22-25, 2011}, + pages = {295--304}, + year = {2011}, + crossref = {DBLP:conf/focs/2011}, + timestamp = {Tue, 16 Dec 2014 09:57:24 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@proceedings{DBLP:conf/focs/2011, + editor = {Rafail Ostrovsky}, + title = {{IEEE} 52nd Annual Symposium on Foundations of Computer Science, {FOCS} + 2011, Palm Springs, CA, USA, October 22-25, 2011}, + publisher = {{IEEE} Computer Society}, + year = {2011}, + isbn = {978-1-4577-1843-4}, + timestamp = {Mon, 15 Dec 2014 18:48:45 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@inproceedings{pw12, + author = {Eric Price and + David P. Woodruff}, + title = {Applications of the Shannon-Hartley theorem to data streams and + sparse recovery}, + booktitle = {Proceedings of the 2012 {IEEE} International Symposium on Information + Theory, {ISIT} 2012, Cambridge, MA, USA, July 1-6, 2012}, + pages = {2446--2450}, + year = {2012}, + crossref = {DBLP:conf/isit/2012}, + timestamp = {Mon, 01 Oct 2012 17:34:07 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@proceedings{DBLP:conf/isit/2012, + title = {Proceedings of the 2012 {IEEE} International Symposium on Information + Theory, {ISIT} 2012, Cambridge, MA, USA, July 1-6, 2012}, + publisher = {{IEEE}}, + year = {2012}, + isbn = {978-1-4673-2580-6}, + timestamp = {Mon, 01 Oct 2012 17:33:45 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{Leskovec:2010, + author = {Jure Leskovec and + Deepayan Chakrabarti and + Jon M. Kleinberg and + Christos Faloutsos and + Zoubin Ghahramani}, + title = {Kronecker Graphs: An Approach to Modeling Networks}, + journal = {Journal of Machine Learning Research}, + volume = {11}, + pages = {985--1042}, + year = {2010}, + timestamp = {Thu, 22 Apr 2010 13:26:26 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{Holme:2002, + author= {Petter Holme and Beom Jun Kim}, + title = {Growing scale-free networks with tunable clustering}, + journal = {Physical review E}, + volume = {65}, + issue = {2}, + pages = {026--107}, + year = {2002} +} + + +@article{watts:1998, + Annote = {10.1038/30918}, + Author = {Watts, Duncan J. and Strogatz, Steven H.}, + Date = {1998/06/04/print}, + Isbn = {0028-0836}, + Journal = {Nature}, + Number = {6684}, + Pages = {440--442}, + Read = {0}, + Title = {Collective dynamics of `small-world' networks}, + Volume = {393}, + Year = {1998}, +} + +@article{barabasi:2001, + author = {R{\'{e}}ka Albert and + Albert{-}L{\'{a}}szl{\'{o}} Barab{\'{a}}si}, + title = {Statistical mechanics of complex networks}, + journal = {CoRR}, + volume = {cond-mat/0106096}, + year = {2001}, + timestamp = {Mon, 05 Dec 2011 18:05:15 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + + +@article{gomezbalduzzi:2011, + author = {Manuel Gomez{-}Rodriguez and + David Balduzzi and + Bernhard Sch{\"{o}}lkopf}, + title = {Uncovering the Temporal Dynamics of Diffusion Networks}, + journal = {CoRR}, + volume = {abs/1105.0697}, + year = {2011}, + timestamp = {Mon, 05 Dec 2011 18:05:23 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{Nowell08, + author = {Liben-Nowell, David and Kleinberg, Jon}, + eprint = {http://www.pnas.org/content/105/12/4633.full.pdf+html}, + journal = {Proceedings of the National Academy of Sciences}, + keywords = {SNA graph networks}, + number = 12, + pages = {4633-4638}, + timestamp = {2008-10-09T10:32:56.000+0200}, + title = {{Tracing information flow on a global scale using Internet chain-letter data}}, + volume = 105, + year = 2008 +} + +@inproceedings{Leskovec07, + author = {Jure Leskovec and + Mary McGlohon and + Christos Faloutsos and + Natalie S. Glance and + Matthew Hurst}, + title = {Patterns of Cascading Behavior in Large Blog Graphs}, + booktitle = {Proceedings of the Seventh {SIAM} International Conference on Data + Mining, April 26-28, 2007, Minneapolis, Minnesota, {USA}}, + pages = {551--556}, + year = {2007}, + timestamp = {Wed, 12 Feb 2014 17:08:15 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + + +@inproceedings{AdarA05, + author = {Eytan Adar and + Lada A. Adamic}, + title = {Tracking Information Epidemics in Blogspace}, + booktitle = {2005 {IEEE} / {WIC} / {ACM} International Conference on Web Intelligence + {(WI} 2005), 19-22 September 2005, Compiegne, France}, + pages = {207--214}, + year = {2005}, + timestamp = {Tue, 12 Aug 2014 16:59:16 +0200}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@inproceedings{Kleinberg:00, + author = {Jon M. Kleinberg}, + title = {The small-world phenomenon: an algorithm perspective}, + booktitle = {Proceedings of the Thirty-Second Annual {ACM} Symposium on Theory + of Computing, May 21-23, 2000, Portland, OR, {USA}}, + pages = {163--170}, + year = {2000}, + timestamp = {Thu, 16 Feb 2012 12:06:08 +0100}, + bibsource = {dblp computer science bibliography, http://dblp.org} +} + +@article{zhang2014, + title={Confidence intervals for low dimensional parameters in high dimensional + linear models}, + author={Zhang, Cun-Hui and Zhang, Stephanie S}, + journal={Journal of the Royal Statistical Society: Series B (Statistical + Methodology)}, + volume={76}, + number={1}, + pages={217--242}, + year={2014}, + publisher={Wiley Online Library} +} + +@article{javanmard2014, + title={Confidence intervals and hypothesis testing for high-dimensional + regression}, + author={Javanmard, Adel and Montanari, Andrea}, + journal={The Journal of Machine Learning Research}, + volume={15}, + number={1}, + pages={2869--2909}, + year={2014}, + publisher={JMLR. org} +} + +@article{donoho2006compressed, + title={Compressed sensing}, + author={Donoho, David L}, + journal={Information Theory, IEEE Transactions on}, + volume={52}, + number={4}, + pages={1289--1306}, + year={2006}, + publisher={IEEE} +} + +@article{candes2006near, + title={Near-optimal signal recovery from random projections: Universal + encoding strategies?}, + author={Candes, Emmanuel J and Tao, Terence}, + journal={Information Theory, IEEE Transactions on}, + volume={52}, + number={12}, + pages={5406--5425}, + year={2006}, + publisher={IEEE} +} + +@article{bickel2009simultaneous, + title={Simultaneous analysis of Lasso and Dantzig selector}, + author={Bickel, Peter J and Ritov, Ya'acov and Tsybakov, Alexandre B}, + journal={The Annals of Statistics}, + pages={1705--1732}, + year={2009}, + publisher={JSTOR} +} + +@article{bagnoli2005log, + title={Log-concave probability and its applications}, + author={Bagnoli, Mark and Bergstrom, Ted}, + journal={Economic theory}, + volume={26}, + number={2}, + pages={445--469}, + year={2005}, + publisher={Springer} +} + + |
