An Agnostic View on the Cost of Overfitting in (Kernel) Ridge Regression

We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an "agnostic" view in the following sense: we consider the cost as a function of sample size for any target function, even if the sample size is not large enough for consistency or the target is outside the RKHS. We analyze the cost of overfitting under a Gaussian universality ansatz using recently derived (non-rigorous) risk estimates in terms of the task eigenstructure. Our analysis provides a more refined characterization of benign, tempered and catastrophic overfitting (qv Mallinar et al. 2022)

Acid/base-triggered switching of circularly polarized luminescence and electronic circular dichroism in organic and organometallic helicenes.

Electronic circular dichroism and circularly polarized luminescence acid/base switching activity has been demonstrated in helicene-bipyridine proligand 1 a and in its “rollover” cycloplatinated derivative 2 a. Whereas proligand 1 a displays a strong bathochromic shift (>160 nm) of the nonpolarized and circularly polarized luminescence upon protonation, complex 2 a displays slightly stronger emission. This strikingly different behavior between singlet emission in the organic helicene and triplet emission in the organometallic derivative has been rationalized by using quantum-chemical calculations. The very large bathochromic shift of the emission observed upon protonation of azahelicene-bipyridine 1 a has been attributed to the decrease in aromaticity (promoting a charge-transfer-type transition rather than a π–π* transition) as well as an increase in the HOMO–LUMO character of the transition and stabilization of the LUMO level upon protonation

Acid/base-triggered switching of circularly polarized luminescence and electronic circular dichroism in organic and organometallic helicenes

Electronic circular dichroism and circularly polarized luminescence acid/base switching activity has been demonstrated in helicene-bipyridine proligand 1 a and in its “rollover” cycloplatinated derivative 2 a. Whereas proligand 1 a displays a strong bathochromic shift (>160 nm) of the nonpolarized and circularly polarized luminescence upon protonation, complex 2 a displays slightly stronger emission. This strikingly different behavior between singlet emission in the organic helicene and triplet emission in the organometallic derivative has been rationalized by using quantum-chemical calculations. The very large bathochromic shift of the emission observed upon protonation of azahelicene-bipyridine 1 a has been attributed to the decrease in aromaticity (promoting a charge-transfer-type transition rather than a π–π* transition) as well as an increase in the HOMO–LUMO character of the transition and stabilization of the LUMO level upon protonation

Regularized fitted Q-iteration: application to planning

We consider planning in a Markovian decision problem, i.e., the problem of finding a good policy given access to a generative model of the environment. We propose to use fitted Q-iteration with penalized (or regularized) least-squares regression as the regression subroutine to address the problem of controlling model-complexity. The algorithm is presented in detail for the case when the function space is a reproducing kernel Hilbert space underlying a user-chosen kernel function. We derive bounds on the quality of the solution and argue that data-dependent penalties can lead to almost optimal performance. A simple example is used to illustrate the benefits of using a penalized procedure

Thermal Resonance in Signal Transmission

We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems.Comment: To appear in Phys. Rev.

Exploiting the bin-class histograms for feature selection on discrete data

In machine learning and pattern recognition tasks, the use of feature discretization techniques may have several advantages. The discretized features may hold enough information for the learning task at hand, while ignoring minor fluctuations that are irrelevant or harmful for that task. The discretized features have more compact representations that may yield both better accuracy and lower training time, as compared to the use of the original features. However, in many cases, mainly with medium and high-dimensional data, the large number of features usually implies that there is some redundancy among them. Thus, we may further apply feature selection (FS) techniques on the discrete data, keeping the most relevant features, while discarding the irrelevant and redundant ones. In this paper, we propose relevance and redundancy criteria for supervised feature selection techniques on discrete data. These criteria are applied to the bin-class histograms of the discrete features. The experimental results, on public benchmark data, show that the proposed criteria can achieve better accuracy than widely used relevance and redundancy criteria, such as mutual information and the Fisher ratio

Theoretical description of hydrogen bonding in oxalic acid dimer and trimer based on the combined extended-transition-state energy decomposition analysis and natural orbitals for chemical valence (ETS-NOCV)

In the present study we have analyzed hydrogen bonding in dimer and trimer of oxalic acid, based on a recently proposed charge and energy decomposition scheme (ETS-NOCV). In the case of a dimer, two conformations, α and β, were considered. The deformation density contributions originating from NOCV’s revealed that the formation of hydrogen bonding is associated with the electronic charge deformation in both the σ—(Δρσ) and π-networks (Δρπ). It was demonstrated that σ-donation is realized by electron transfer from the lone pair of oxygen on one monomer into the empty \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_{H - O}^*$$\end{document} orbital of the second oxalic acid fragment. In addition, a covalent contribution is observed by the density transfer from hydrogen of H-O group in one oxalic acid monomer to the oxygen atom of the second fragment. The resonance assisted component (Δρπ), is based on the transfer of electron density from the π—orbital localized on the oxygen of OH on one oxalic acid monomer to the oxygen atom of the other fragment. ETS-NOCV allowed to conclude that the σ(O---HO) component is roughly eight times as important as π (RAHB) contribution in terms of energetic estimation. The electrostatic factor (ΔEelstat) is equally as important as orbital interaction term (ΔEorb). Finally, comparing β-dimer of oxalic acid with trimer we found practically no difference concerning each of the O---HO bonds, neither qualitative nor quantitative

Mesothelioma and asbestosis in a young woman following occupational asbestos exposure: Short latency and long survival: Case Report

A 27-year-old female white-collar worker was diagnosed in 1998 with mesothelioma eight and one-half years following first exposure as a bystander to debris in a site in which asbestos-containing building materials were being dismantled and rebuilding work took place. Prodromal back pain had been present for a year and a half. She underwent extrapleural pneumectomy and received an intrapleural infusion of cisplatin post-operatively. Exposure to asbestos was verified by contemporary reports and lung biopsy, which demonstrated asbestos bodies and microscopic interstitial fibrosis -conforming evidence for asbestosis. The patient is alive and well 12 years after diagnosis and 14 years after onset of symptoms. The combination of an extremely short latency period and long survival following occupational exposure to asbestos dust is unique

The Convex Geometry of Linear Inverse Problems

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems. The class of simple models considered are those formed as the sum of a few atoms from some (possibly infinite) elementary atomic set; examples include well-studied cases such as sparse vectors and low-rank matrices, as well as several others including sums of a few permutations matrices, low-rank tensors, orthogonal matrices, and atomic measures. The convex programming formulation is based on minimizing the norm induced by the convex hull of the atomic set; this norm is referred to as the atomic norm. The facial structure of the atomic norm ball carries a number of favorable properties that are useful for recovering simple models, and an analysis of the underlying convex geometry provides sharp estimates of the number of generic measurements required for exact and robust recovery of models from partial information. These estimates are based on computing the Gaussian widths of tangent cones to the atomic norm ball. When the atomic set has algebraic structure the resulting optimization problems can be solved or approximated via semidefinite programming. The quality of these approximations affects the number of measurements required for recovery. Thus this work extends the catalog of simple models that can be recovered from limited linear information via tractable convex programming