Understanding Machine Learning From Theory to Algorithms 1st Edition Shwartz Solutions Manual

By Alon Gonen. 2015

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In Statistical Learning Theory

Citations in the corpus

GAIT: A Geometric Approach to Information Theory (2019, background): “Information theory is ubiquitous in modern machine learning: from variable selection via information gain in decision trees (Ben-David and Shalev-Shwartz, 2014), to using entropy as a regularizer in reinforcement learning (Fox et al.”
Detection and Continual Learning of Novel Face Presentation Attacks (2021, methodology): “If n0 is large enough, the selected deep network structure is suitable, and observed data during testing are drawn from the training distribution q(x) then the model will generalize well during execution according to theoretical guarantees of PAC-learning framework [31].”
Preserving Statistical Validity in Adaptive Data Analysis (2014, background): “The classical approach in theoretical machine learning to ensure that empirical estimates generalize to the underlying distribution is based on the various notions of complexity of the set of functions output by the algorithm, most notably the VC dimension (see [31] or [39] for a textbook introducti”
Lagrange Coded Computing: Optimal Design for Resiliency, Security and Privacy (2018, background): “Another general class of functions arises from gradient decent algorithms and their variants, which are the workhorse of today’s learning tasks [32].”
The landscape of empirical risk for nonconvex losses (2016, background): “noisy half-spaces) is a very well-studied topic in machine learning, and many of its aspects have been investigated in depth, see for instance [3, 17] for readable introductions.”
SGD Learns the Conjugate Kernel Class of the Network (2017, methodology): “ F M MW~ t kW~ tk F kW~ t F >M Where r‘ yt (W t 1x t) is a sub-gradient of ‘ yt at W t 1x t. After T = M2L2 2 iterations the loss in expectation would be at most (see for instance Chapter 14 in [30]). In particular, there exists a sequence of at most M2L2 2 gradient steps that attains a solution ”
Accelerated proximal stochastic dual coordinate ascent for regularized loss minimization (2013, methodology): “Remark 3 Usually, the hinge-loss is used as a convex surrogate for the zero-one loss (see for example [23], section 12.”
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory (2017, background): “optimization problems of the form min x∈Rn 1 m Xm i=1 fi(x) +g(x), (2.4) where fi is a loss function and ga regularizer. Problems of this form are of key importance in machine learning and statistics [66]. Let fi(x) = 0 if Ai:x= bi and fi(x) = +∞otherwise, further let g(x) = kx−x 0k2 B. In this sett”
Revisiting Meta-Learning as Supervised Learning (2020, methodology): “The metatraining set Dmeta-tr thus becomes {(Dtrj , Dvalj)}Nmetaj=1 and ERM in Equation 5 can be re-written accordingly as (with constants ignored) ĝ = arg ming∈G Nmeta∑ j=1 LV j(g(Dtrj)) = arg ming∈G Nmeta∑ j=1 M∑ m=1 l(g(Dtrj)(xjm), yjm).”
A Generalization Theory of Gradient Descent for Learning Over-parameterized Deep ReLU Networks (2019, methodology): “We consider the empirical Rademacher complexity (Bartlett and Mendelson, 2002; Mohri et al., 2018; Shalev-Shwartz and Ben-David, 2014) of FpWp0q, τq defined as follows”
SelfieBoost: A Boosting Algorithm for Deep Learning (2014, background): “One of the most successful approaches for training neural networks is Stochastic Gradient Descent (SGD) and its variants (see for example [14, 4, 1, 15, 24, 25, 21]).”