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The landscape of empirical risk for nonconvex losses
2018
Annals of Statistics
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In this paper, we focus on the case of nonconvex losses. Classical empirical process theory implies uniform convergence of the empirical (or sample) risk to the population risk. ...
Uniform convergence of the empirical risk. Let R(θ ) = E R n (θ) denote the population risk. ...
doi:10.1214/17-aos1637
fatcat:646bhqjaovclbdqcsuof2esoam
A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks
[article]
2018
arXiv
pre-print
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An explosion of high-throughput DNA sequencing in the past decade has led to a surge of interest in population-scale inference with whole-genome data. ...
Recent work in population genetics has centered on designing inference methods for relatively simple model classes, and few scalable general-purpose inference techniques exist for more realistic, complex ...
Minimizing nonconvex population risk
from rough empirical risk. arXiv preprint arXiv:1803.09357, 2018.
[28] P. Fearnhead and D. Prangle. ...
arXiv:1802.06153v2
fatcat:uv63a54qrfghzgotg5q3l2cv2a
Application and Comparative Study of Optimization Algorithms in Financial Investment Portfolio Problems
2021
Mobile Information Systems
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Portfolio theory mainly studies how to optimize the allocation of assets under the premise of maximizing expected returns and minimizing investment risks. ...
The results show that the genetic algorithm model is superior to the quadratic programming method in terms of risk control. ...
function called P(o) define the fitness function in a population as the population function whose value is f(f > 0). (4) Calculate the fitness value of each chromosome. (5) rough the selection operation ...
doi:10.1155/2021/3462715
fatcat:76tpk34nvvbexjafopzcgra3hq
Patterns, predictions, and actions: A story about machine learning
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2102.05242v1 fatcat:ghg6hn4djvdszkwpkg37lul5nm
We invite readers from all backgrounds; some experience with probability, calculus, and linear algebra suffices. ...
Empirical risk minimization is commonly used as a proxy for minimizing the unknown population risk. But how good is this proxy? ...
Empirical risk minimization seeks to find a predictor f * in a specified class F that minimizes the empirical risk: f * = arg min f ∈F R S [ f ] In the context of empirical risk minimization, the empirical ...
arXiv:2102.05242v2
fatcat:wy47g4fojnfuxngklyewtjtqdi
A nonparametric estimator of population structure unifying admixture models and principal components analysis
[article]
2017
bioRxiv
pre-print
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Central to this strategy is the observation that all models belonging to this constrained space of solutions are risk-minimizing and have equal likelihood, rendering any additional optimization unnecessary ...
We introduce a simple and computationally efficient method for fitting the admixture model of genetic population structure, called ALStructure. ...
While problem (15) is nonconvex as stated, the following two subproblems are convex: minimize P ||F − P Q|| (16) subject to: minimize Q ||F − P Q|| (17) subject to: That (16) and (17) are convex ...
doi:10.1101/240812
fatcat:fqgn4ozadrajxk47qjbl55aypq
A Likelihood-Free Estimator of Population Structure Bridging Admixture Models and Principal Components Analysis
2019
Genetics
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Central to this strategy is the observation that all models belonging to this constrained space of solutions are risk-minimizing and have equal likelihood, rendering any additional optimization unnecessary ...
Our approach differs fundamentally from other existing methods for estimating admixture, which aim to fit the admixture model directly by searching for parameters that maximize the likelihood function ...
An algorithm with provable convergence: While problem (10) is nonconvex as stated, the following two subproblems are convex: minimize P F 2 PQ (11) subject to: h minimize Q F 2 PQ (12) subject to: 4 That ...
doi:10.1534/genetics.119.302159
pmid:31028112
pmcid:PMC6707457
fatcat:ww7amgk6qzhhncssjkfwvoscba
Cubic Regularization with Momentum for Nonconvex Optimization
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1810.03763v1 fatcat:wgeoqk5ubra7repavy6mc66rne
Theoretically, we prove that CR under momentum achieves the best possible convergence rate to a second-order stationary point for nonconvex optimization. ...
However, such a successful acceleration technique has not yet been proposed for second-order algorithms in nonconvex optimization.In this paper, we apply the momentum scheme to cubic regularized (CR) Newton's ...
Minimizing nonconvex population risk from rough empirical risk. arXiv:1803.09357. Jin, C., Netrapalli, P., and Jordan, M. I. (2017). ...
arXiv:1810.03763v2
fatcat:cyw6ycinu5bblnxel4ytqxc4om
Exchange Rate Forecasting Based on Deep Learning and NSGA-II Models
2021
Computational Intelligence and Neuroscience
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the risk. ...
Finally, the order of filling C from large to small is continued according to the crowd distance of individuals in Fi until the population number reaches N. ...
doi:10.1155/2021/2993870
pmid:34603429
pmcid:PMC8481046
fatcat:yxu5x6qsnjelxlltoejocjxyd4
Efficiency Assessment of Existing Pumping/Hydraulic Network Systems to Mitigate Flooding in Low-Lying Coastal Regions under Different Scenarios of Sea Level Rise: The Mazzocchio Area Study Case
2018
Water
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the considered area; (b) to minimize the pumping power necessary to mitigate the flooding. ...
Rising of the sea level and/or heavy rainfall intensification significantly enhance the risk of flooding in low-lying coastal reclamation areas. ...
In accordance with these definitions, a genetic algorithm deals with a population of points, and hence multiple Pareto optimal solutions can be obtained from a population in a single run. ...
doi:10.3390/w10070820
fatcat:vmto5my3v5hbvibeid2xmg3tfq
Efficiently testing local optimality and escaping saddles for ReLU networks
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1809.10858v1 fatcat:te3rijouuzf6hd5vm6wq6x5maq
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. ...
For the last QP, we show that our specific problem can be solved efficiently, in spite of nonconvexity. ...
Whenever the point z * is clear (e.g. our algorithm), we will omit (z * ) from f (z * ). Next, we define second-order stationary points for the empirical risk R. ...
arXiv:1809.10858v2
fatcat:kxg2rxnlrrcgrjck64w457xmwi
On surrogate loss functions and f -divergences
2009
Annals of Statistics
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We present conditions on loss functions such that empirical risk minimization yields Bayes consistency when both the discriminant function and the quantizer are estimated. ...
The goal of binary classification is to estimate a discriminant function γ from observations of covariate vectors and corresponding binary labels. ...
risk minimization procedures can be applied. ...
doi:10.1214/08-aos595
fatcat:cjqpk3d7grfjziw64ymt66rhy4
Support Vector Machines with Applications
2006
Statistical Science
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The SVMs operate within the framework of regularization theory by minimizing an empirical risk in a well-posed and consistent way. ...
The benefits of empirical convex risk minimization are not just computational. ...
In contrast, while the VC dimension is central to the analysis of methods that minimize the empirical 0-1 risk, it is not relevant to SVMs. ...
doi:10.1214/088342306000000493
fatcat:xzlbp2yozvb6xezpamfqo2mzxy
Quality / capacity substitution in the delivery of mental health care
1988
Socio-Economic Planning Sciences
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This research has been supported from U.S. Public Health Service grant MH41212. ...
In any case, this stands as a preliminary exercise, and its value is primarily that of showing that the nonconvexity is present in models that possess a good deal of empirical realism. ...
In the first place, it limits the potential of insurance for providing private care, because the expenses of future treatments are not insurable risks. ...
doi:10.1016/0038-0121(88)90016-x
fatcat:vhf63bsfjvcvlf3qssu7xzkwvm
Statistical Challenges with High Dimensionality: Feature Selection in Knowledge Discovery
[article]
2006
arXiv
pre-print
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The persistence property in risk minimization is also addressed. The applicability of such a theory and method to diverse statistical problems is demonstrated. ...
The challenges of high-dimensionality arise in diverse fields of sciences and the humanities, ranging from computational biology and health studies to financial engineering and risk management. ...
The penalized least squares method will be further extended to penalized empirical risk minimization for machine learning in Section 6.4. ...
arXiv:math/0602133v1
fatcat:vgzkjoatnrhqfp3sceio2zfeuu
Statistical Modeling of Networked Solar Resources for Assessing and Mitigating Risk of Interdependent Inverter Tripping Events in Distribution Grids
[article]
2019
arXiv
pre-print
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To quantify this risk utilities need to solve the interactive equations of tripping events for networked PVs in real-time. ...
It is speculated that higher penetration of inverter-based distributed photo-voltaic (PV) power generators can increase the risk of tripping events due to voltage fluctuations. ...
Furthermore, it is demonstrated that the proposed model can be used for identifying regime shifts in tripping events and designing countermeasures to minimize risk of solar power curtailment. ...
arXiv:1908.01129v2
fatcat:o7536he3hzdozngsufe2jyfjty
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