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Online Sampling from Log-Concave Distributions [article]

Holden Lee, Oren Mangoubi, Nisheeth K. Vishnoi
2019 arXiv   pre-print
., f_T, we study the problem of sampling from the Gibbs distribution π_t ∝ e^-∑_k=0^tf_k for each epoch t in an online manner.  ...  Our main result is an algorithm that generates roughly independent samples from π_t for every epoch t and, under mild assumptions, makes polylog(T) gradient evaluations per epoch.  ...  Non-compact distributions One can also consider the problem of sampling from log-densities which are a sum of T functions with compact support (online sampling from such distributions was considered in  ... 
arXiv:1902.08179v4 fatcat:irm6yhm7zrewxkud37xni6zgzi

Fast rates with high probability in exp-concave statistical learning [article]

Nishant A. Mehta
2016 arXiv   pre-print
We further show that a regret bound for any online learner in this setting translates to a high probability excess risk bound for the corresponding online-to-batch conversion of the online learner.  ...  Lastly, we present two high probability bounds for the exp-concave model selection aggregation problem that are quantile-adaptive in a certain sense.  ...  Introduction In the statistical learning problem, a learning agent observes a samples of n points Z 1 , . . . , Z n drawn i.i.d. from an unknown distribution P over an outcome space Z.  ... 
arXiv:1605.01288v4 fatcat:mvmduzplwzcknifiwccbxhqixa

On the Power of Localized Perceptron for Label-Optimal Learning of Halfspaces with Adversarial Noise [article]

Jie Shen
2021 arXiv   pre-print
Our main contribution is a Perceptron-like online active learning algorithm that runs in polynomial time, and under the conditions that the marginal distribution is isotropic log-concave and ν = Ω(ϵ),  ...  distributions.  ...  log-concave distributions and are O(d 1/ǫ 4 ) for uniform distributions.  ... 
arXiv:2012.10793v3 fatcat:4w3t4m3ij5es3hddwbcxkohhpm

Online Revenue Maximization for Server Pricing [article]

Shant Boodaghians, Federico Fusco, Stefano Leonardi, Yishay Mansour, Ruta Mehta
2019 arXiv   pre-print
If the distribution of agent's type is only learned from observing the jobs that are executed, we prove that a polynomial number of samples is sufficient to obtain a near-optimal truthful pricing strategy  ...  One agent/job arrives at every time step, with parameters drawn from an underlying unknown distribution.  ...  A Log-Concave Distributions In Section 3.3, we sought to show that if the value of a random job has a log-concave distribution, then the optimal policy will be monotone.  ... 
arXiv:1906.09880v3 fatcat:wj4rmjco2neqfjlto4lc45n37e

Dimension-free Information Concentration via Exp-Concavity [article]

Ya-Ping Hsieh, Volkan Cevher
2018 arXiv   pre-print
In this work, we prove that if the potentials of the log-concave distribution are exp-concave, which is a central notion for fast rates in online and statistical learning, then the concentration of information  ...  Recently, it is discovered that the information content of a log-concave distribution concentrates around their differential entropy, albeit with an unpleasant dependence on the ambient dimension.  ...  Acknowledgments This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement n o 725594 -time-data  ... 
arXiv:1802.09301v1 fatcat:2ahy2alzvrd6jk5elpozq4vhd4

Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions [article]

Alexandre Belloni, Tengyuan Liang, Hariharan Narayanan, Alexander Rakhlin
2015 arXiv   pre-print
The problem is reduced to sampling from an approximately log-concave distribution using the Hit-and-Run method, which is shown to have the same O^* complexity as sampling from log-concave distributions  ...  In addition to extend the analysis for log-concave distributions to approximate log-concave distributions, the implementation of the 1-dimensional sampler of the Hit-and-Run walk requires new methods and  ...  According to Lemmas 5, 6, 7, the unidimensional sampling method produces a sample from a distribution that is close to the desired β-log-concave distribution.  ... 
arXiv:1501.07242v2 fatcat:nc3l4akcmvfsha2g4wodgsuj6q

Integral Mixability: a Tool for Efficient Online Aggregation of Functional and Probabilistic Forecasts [article]

Alexander Korotin, Vladimir V'yugin, Evgeny Burnaev
2020 arXiv   pre-print
In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts.  ...  We adapt basic mixable (and exponentially concave) loss functions to compare functional predictions and prove that these adaptations are also mixable (exp-concave).  ...  Additionally, it provides a natural way to sample from the aggregated distribution γ, i.e. sampling from t ∼ Uniform[0, 1] and applying Q. Now we prove the lemma. Proof.  ... 
arXiv:1912.07048v3 fatcat:4hesa7rhwfezlexrljec773fsa

First-Come-First-Served for Online Slot Allocation and Huffman Coding [article]

Monik Khare and Claire Mathieu and Neal E. Young
2013 arXiv   pre-print
Requests for items are drawn i.i.d. from a fixed but hidden probability distribution p.  ...  The optimal competitive ratios for any online algorithm are 1+H(n-1) ~ ln n for general costs and 2 for concave costs.  ...  F 's concavity gives E[F (j i )] ≤ F (E[j i ]) ≤ F (1/f i ). Recall c j = log 2 j + O(log log j).  ... 
arXiv:1307.5296v2 fatcat:y23qib72o5fvdlq3bnygtktdhm

First Come First Served for Online Slot Allocation and Huffman Coding [chapter]

Monik Khare, Claire Mathieu, Neal E. Young
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
Requests for items are drawn i.i.d. from a fixed but hidden probability distribution p.  ...  The optimal competitive ratios for any online algorithm are 1 + H n−1 ∼ ln n for general costs and 2 for concave costs.  ...  F 's concavity gives E[F (j i )] ≤ F (E[j i ]) ≤ F (1/f i ). Recall c j = log 2 j + O(log log j).  ... 
doi:10.1137/1.9781611973402.33 dblp:conf/soda/KhareMY14 fatcat:rbv6awu4abdqrakzorek6rppim

Online Variance Reduction with Mixtures [article]

Zalán Borsos, Sebastian Curi, Kfir Y. Levy, Andreas Krause
2019 arXiv   pre-print
While these sampling distributions are fixed, the mixture weights are adapted during the optimization process.  ...  In this work, we propose a new framework for variance reduction that enables the use of mixtures over predefined sampling distributions, which can naturally encode prior knowledge about the data.  ...  This is a deviation from our presentation, where we relied on fixed sampling distributions.  ... 
arXiv:1903.12416v1 fatcat:avpyaq5v2fa3xavqdx65c7o4je

House Price Momentum and Strategic Complementarity

Adam M. Guren
2018 Journal of Political Economy  
I provide new micro-empirical evidence that the demand curve faced by sellers is concave and show using a search model calibrated to the micro evidence that concave demand amplifies momentum by a factor  ...  Sellers have an incentive not to set a unilaterally high or low list price because the demand curve they face is concave in relative price: increasing the list price of an above-averaged priced house rapidly  ...  Binned scatter plots in online appendix C show that most of the difference across samples is from extreme quantiles that do not drive concavity in the IV specification.  ... 
doi:10.1086/697207 fatcat:mwyl2n3od5hw7dm26pjk2v3moy

Query Auditing for Protecting Max/Min Values of Sensitive Attributes in Statistical Databases [chapter]

Ta Vinh Thong, Levente Buttyán
2012 Lecture Notes in Computer Science  
The work presented in this paper has been carried out in the context of the CHIRON Project (www.chiron-project.eu), which receives funding from the European Community in the context of the ARTEMIS Programme  ...  In addition, our online simulatable auditor is based on random sampling, and we want to apply directly the method of Lovasz [9] on effective sampling from log-concave distributions.  ...  The truncated version of log-concave distribution is also log-concave. 2. If G is a log-concave distribution then the joint distribution G n is also logconcave. 3.  ... 
doi:10.1007/978-3-642-32287-7_17 fatcat:54wazae7mbahpdyu2p5t2tmkyq

An Online Learning Approach to Generative Adversarial Networks [article]

Paulina Grnarova and Kfir Y. Levy and Aurelien Lucchi and Thomas Hofmann and Andreas Krause
2017 arXiv   pre-print
Building on ideas from online learning we propose a novel training method named Chekhov GAN 1 .  ...  Although GANs can accurately model complex distributions, they are known to be difficult to train due to instabilities caused by a difficult minimax optimization problem.  ...  We sample points x from the data distribution p data with different probabilities for each mode.  ... 
arXiv:1706.03269v1 fatcat:coqc4435iret7cs6mmqgws4dlu

Efficient iterative policy optimization [article]

Nicolas Le Roux
2016 arXiv   pre-print
This is done by approximating the expected policy reward as a sequence of concave lower bounds which can be efficiently maximized, drastically reducing the number of policy updates required to achieve  ...  Without the ability to exactly compute J a , we must resort to sampling to get an estimate of both J and its gradient. These samples can come from p(·|θ) or from another distribution.  ...  Thus, in the spirit of off-policy learning, we have replaced extra sampling with importance sampling. When, and only when, variance starts to be too high, can we sample from the new distribution.  ... 
arXiv:1612.08967v1 fatcat:shodjcc4pza7zhzkx2tkaay2py

Bregman divergences based on optimal design criteria and simplicial measures of dispersion

Luc Pronzato, Henry P. Wynn, Anatoly Zhigljavsky
2019 Statistical Papers  
A general construction is given based on defining a directional derivative of a function φ from one distribution to the other whose concavity or strict concavity influences the properties of the resulting  ...  In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices  ...  The hypothesis H0 that both samples come from distributions having the same mean and covariance is clearly rejected.  ... 
doi:10.1007/s00362-018-01082-8 fatcat:2q3jwknozvhvjohaqa7hriadma
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