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Distribution Free Uncertainty for the Minimum Norm Solution of Over-parameterized Linear Regression [article]

Koby Bibas, Meir Feder
2021 arXiv   pre-print
We utilize the recently proposed predictive normalized maximum likelihood (pNML) learner which is the min-max regret solution for the distribution-free setting.  ...  We investigate over-parameterized linear regression models focusing on the minimum norm solution: This is the solution with the minimal norm that attains a perfect fit to the training set.  ...  For sequential prediction this learner was suggested by Roos and Rissanen (2008) and was termed the conditional normalized maximum likelihood (CNML).  ... 
arXiv:2102.07181v2 fatcat:2yzkmnl4kbesphmxfghbcrgtgq

A Survey of Algorithms and Analysis for Adaptive Online Learning [article]

H. Brendan McMahan
2015 arXiv   pre-print
Our regret bounds are proved in the most general form, holding for arbitrary norms and non-smooth regularizers with time-varying weight.  ...  Adaptivity can be used to prove regret bounds that hold on every round, and also allows for data-dependent regret bounds as in AdaGrad-style algorithms (e.g., Online Gradient Descent with adaptive per-coordinate  ...  Here t is for example a loss function measuring the prediction error on the tth training example for a model parameterized by x t .  ... 
arXiv:1403.3465v3 fatcat:joigpxul4rbhlmmqdnxckvoyye

A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning [article]

Sijia Liu, Pin-Yu Chen, Bhavya Kailkhura, Gaoyuan Zhang, Alfred Hero, Pramod K. Varshney
2020 arXiv   pre-print
In this paper, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles and recent advances in convergence analysis.  ...  It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations.  ...  However, it increases the computation cost due to the need to solve nested regression problems. B. ZO optimization with black-box constraints.  ... 
arXiv:2006.06224v2 fatcat:fx624eqhifbqpp5hbd5a5cmsny

Online Optimization in Dynamic Environments [article]

Eric C. Hall, Rebecca M. Willett
2016 arXiv   pre-print
This paper describes a dynamic mirror descent framework which addresses this challenge, yielding low theoretical regret bounds and accurate, adaptive, and computationally efficient algorithms which are  ...  The methods are capable of learning and adapting to an underlying and possibly time-varying dynamical model.  ...  The matrix W is then normalized so that its spectral norm is 0.25 for stability.  ... 
arXiv:1307.5944v3 fatcat:jkpa4aomt5ashls2ucbu4ls7su

Transitions, Losses, and Re-parameterizations: Elements of Prediction Games [article]

Parameswaran Kamalaruban
2018 arXiv   pre-print
The insights shed some light on the understanding of the intrinsic barriers of the prediction problems and the design of computationally efficient learning algorithms with strong theoretical guarantees  ...  This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization.  ...  In practice the original convex optimization problem itself can have a regularization term associated with the constraints of the problem and generally it is not preferable to linearize those (possibly  ... 
arXiv:1805.08622v1 fatcat:ymwsxiis2jdyxedgl54y23qb7a

Patterns, predictions, and actions: A story about machine learning [article]

Moritz Hardt, Benjamin Recht
2021 arXiv   pre-print
Throughout, the text discusses historical context and societal impact. We invite readers from all backgrounds; some experience with probability, calculus, and linear algebra suffices.  ...  Self-contained introductions to causality, the practice of causal inference, sequential decision making, and reinforcement learning equip the reader with concepts and tools to reason about actions and  ...  For linear predictors the Euclidean norm provides a natural and often suitable normalization.  ... 
arXiv:2102.05242v2 fatcat:wy47g4fojnfuxngklyewtjtqdi

A maximum-entropy approach to off-policy evaluation in average-reward MDPs [article]

Nevena Lazic, Dong Yin, Mehrdad Farajtabar, Nir Levine, Dilan Gorur, Chris Harris, Dale Schuurmans
2020 arXiv   pre-print
In a more general setting, when the feature dynamics are approximately linear and for arbitrary rewards, we propose a new approach for estimating stationary distributions with function approximation.  ...  For MDPs that are ergodic and linear (i.e. where rewards and dynamics are linear in some known features), we provide the first finite-sample OPE error bound, extending existing results beyond the episodic  ...  D Stationary distribution with large entropy In this paper, we try to find the distribution over states that maximizes the entropy under some linear constraints, and use it as a proxy for the stationary  ... 
arXiv:2006.12620v1 fatcat:v3uohickvjhvnmrhc6wdlmm7gu

Online Learning with (Multiple) Kernels: A Review

Tom Diethe, Mark Girolami
2013 Neural Computation  
In SAA, the above problem is approximated with min w  ...  Neural Computation 25, 567-625 (2013) c 2013 Massachusetts Institute of Technology where R is the regularization function, w is the solution vector, and L is the loss function.  ...  Acknowledgments This work is supported by NCR Financial Solutions Group under the project title "Developments of Multiple Kernel Learning, Algorithmic Efficiency &  ... 
doi:10.1162/neco_a_00406 pmid:23272919 fatcat:7qaklnrirbdftcocoyqonk6tta

Maximum likelihood estimation of a multi-dimensional log-concave density

Madeleine Cule, Richard Samworth, Michael Stewart
2010 Journal of The Royal Statistical Society Series B-statistical Methodology  
We first prove that, with probability 1, there is a unique log-concave maximum likelihood estimatorf n of f.  ...  ., X n be independent and identically distributed random vectors with a (Lebesgue) density f.  ...  We thank Yining Chen for his help with the simulations that are reported in this rejoinder.  ... 
doi:10.1111/j.1467-9868.2010.00753.x fatcat:wtuitpjvvjhn7lkvmvneomi2ra

Technical Program

2021 2020 IEEE Information Theory Workshop (ITW)  
channel with feedback equals the capacity of the same model without secrecy constraint.  ...  multiple-access wiretap channel with degraded message sets (GMAC-WT-DMS) equals the capacity of the same model without secrecy constraint.  ...  Assuming a maximum-likelihood (ML) decoder, we find the best codebook design by minimizing the error probability of the decoder over all codebooks.  ... 
doi:10.1109/itw46852.2021.9457668 fatcat:j425ygeajrbd5esztbe5zgygty

Machine Learning: The Basics [article]

Alexander Jung
2022 arXiv   pre-print
This principle consists of the continuous adaptation of a hypothesis about a phenomenon that generates data. ML methods use a hypothesis to compute predictions for future events.  ...  We believe that thinking about ML as combinations of three components given by data, model, and loss helps to navigate the steadily growing offer for ready-to-use ML methods.  ...  are the maximum likelihood estimators for the mean and variance of a normal (Gaussian) distribution p(x) (see [13, Chapter 2.3.4] ).  ... 
arXiv:1805.05052v17 fatcat:bntuctsunbevxp5v5w4krszcbe

Bayesian binary quantile regression for the analysis of Bachelor-to-Master transition

Cristina Mollica, Lea Petrella
2016 Journal of Applied Statistics  
methods for Predictive and Exploratory Path modeling  ...  Specialized teams Currently the ERCIM WG has over 1150 members and the following specialized teams BM: Bayesian Methodology CODA: Complex data structures and Object Data Analysis CPEP: Component-based  ...  Some new applications to quantile regression methods will be described focusing on first order gradient descent methods for large problems, as well as Kiefer Wolfowitz non-parametric maximum likelihood  ... 
doi:10.1080/02664763.2016.1263835 fatcat:l5eyielgxrct7hq5ljqeej5ccy

How Generative Adversarial Networks and Their Variants Work

Yongjun Hong, Uiwon Hwang, Jaeyoon Yoo, Sungroh Yoon
2019 ACM Computing Surveys  
Finally, we enumerate the GAN variants that are applied to various tasks and other fields for those who are interested in exploiting GAN for their research.  ...  We then focus on how the GAN can be combined with an autoencoder framework.  ...  models [92, 105] , are based on the maximum likelihood principle with a model parametrized by parameters θ.  ... 
doi:10.1145/3301282 fatcat:z2xe6jdh5nd2dmovkes3rav3ke

Optimization Methods for Large-Scale Machine Learning [article]

Léon Bottou, Frank E. Curtis, Jorge Nocedal
2018 arXiv   pre-print
Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved  ...  This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications.  ...  For example, when F is a strictly convex quadratic with minimum and maximum eigenvalues given by c > 0 and L ≥ c, respectively, steepest descent and the heavy ball method each yield a linear rate of convergence  ... 
arXiv:1606.04838v3 fatcat:7gksju7azndy5almouyzycayci

Dueling Posterior Sampling for Preference-Based Reinforcement Learning [article]

Ellen R. Novoseller, Yibing Wei, Yanan Sui, Yisong Yue, Joel W. Burdick
2020 arXiv   pre-print
We prove an asymptotic Bayesian no-regret rate for DPS with a Bayesian linear regression credit assignment model. This is the first regret guarantee for preference-based RL to our knowledge.  ...  system dynamics and the underlying utility function that governs the preference feedback.  ...  Acknowledgments This work was supported by NIH grant EB007615 and an Amazon graduate fellowship.  ... 
arXiv:1908.01289v4 fatcat:uz2vmfgicjc6zfmlbc2oeklf2a
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