Spline Models for Observational Data

By Grace Wahba. 1990

Subfields: Statistics and Probability, Numerical Methods & Scientific Computing

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Citations in the corpus

On the Equivalence between Herding and Conditional Gradient Algorithms (2012, positive): “On the right plot, it turns out that the Sobol sequence is known to achieve the optimal rate of O ( t − 2 ) for k µ − ˆ µ k 2 for the associated Sobolev space (Wahba, 1990).”
Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning (2017, background): “ief regarding the model [7]. A popular a priori belief based on widely observed facts is that the outputs of most naturally occurring systems are smooth with respect to spatial and/or temporal inputs [46]. What often underlie this belief are the laws of physics governing the system Contact : takeru”
Distributional Smoothing with Virtual Adversarial Training (2015, background): “For example, images and time series occurring in nature tend to be smooth with respect to the space and time (Wahba, 1990).”
Estimating treatment effect heterogeneity in randomized program evaluation (2013, methodology): “We choose the optimal values of the tuning parameters, {λZ , λV }, based on a generalized cross-validation (GCV) statistic [Wahba (1990)], so that the model fit is”
Bayesian Learning of Kernel Embeddings (2016, background): “While it is tempting to deﬁne a GP (0 , k θ ( · , · )) prior on µ θ , this is problematic since draws from such prior would almost surely fall outside H k (Wahba, 1990).”
Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, background): “This allows us to identify P † P from k and vice versa (Smola et al., 1998a; Girosi, 1998; Girosi et al., 1995; Girosi and Anzellotti, 1993; Wahba, 1990).”
Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels (2014, methodology): “M L] 2 9 D ec 2 01 We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets.”
Sharp analysis of low-rank kernel matrix approximations (2012, neutral): “First, using the representer theorem, the unique solution f may be found as f = P =1 α i φ ( x i ) (see, e.g., Wahba, 1990; Sch¨olkopf and Smola, 2002; Shawe-Taylor and Cristianini, 2004).”
Kernels for Vector-Valued Functions: a Review (2011, methodology): “Connections between regularization theory and Gaussian process prediction or Bayesian models for prediction have been pointed out elsewhere [78, 105, 82].”
Convolutional Kernel Networks (2014, methodology): “To obtain a finite-dimensional representation, we need to approximate the integral with a weighted finite sum, which is a classical problem in numerical analysis and statistics (see [28] and chapter 8 of [6] for a review).”
On the mathematical foundations of learning (2001, background): “See also [45] for contributions to these matters coming from statistics.”
Kernel dimension reduction in regression (2009, background): “sitive deﬁnite kernels are Hilbert spaces of smooth functions that are “small” enough to yield computationally-tractable procedures, but are rich enough to capture nonparametric phenomena of interest [32], and this computational focus is an important aspect of our work. On the other hand, whereas in”
Clustered Multi-Task Learning: A Convex Formulation (2008, background): “In particular, regularization by squared Euclidean norms or squared Hilbert norms has been thoroughly studied in various settings, leading to eﬃcient practical algorithms based on linear algebra, and to very good theoretical understanding (see, e.g., [1, 2]).”
Testing for Homogeneity with Kernel Fisher Discriminant Analysis (2007, background): “Note that by taking Fourier transforms (P of p, and K of k), the eigenvalues are the same as the one of T (K)1/2C(P )T (K)1/2 and thus p and K plays equivalent roles (Widom, 1963). The following lemma, taken from Widom (1964), gives an upperbound of the eigenvalues in the situation where p and K are”
Optimal Rates for the Regularized Least-Squares Algorithm (2007, methodology): “The RLS algorithm on RKHS of real-valued functions (i.e. when the output space is equal to R) has been extensively studied in the literature, for an account see [33], [30], [17] and references therein.”
Kernel methods in machine learning (2007, neutral): “Here we consider the more general case of minimizing a functional that includes a monotone function of the Hilbert space norm ‖f‖H as a stabilizer (Wahba [148]).”
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates (2013, methodology): “We provide only a very brief coverage of the basics here, referring the reader to one of the many books on the topic (Wahba, 1990; Shawe-Taylor and Cristianini, 2004; Berlinet and Thomas-Agnan, 2004; Gu, 2002) for further details.”
Component selection and smoothing in multivariate nonparametric regression (2006, methodology): “…N ON PARAM ETRIC REG RESSION By Y iLin1 and H ao H elen Zhang2 University ofW isconsin{M adison and North Carolina State University W e propose a new m ethod for m odelselection and m odel tting in m ultivariate nonparam etric regression m odels,in the fram ework of sm oothing spline ANOVA.”