Search

In this paper, we delve into the statistical analysis of the fitted Q-evaluation (FQE) method, which focuses on estimating the value of a target policy using offline data generated by some behavior policy. We provide a comprehensive theoretical understanding of FQE estimators under both parameteric and nonparametric models on the $Q$-function. Specifically, we address three key questions related to FQE that remain largely unexplored in the current literature: (1) Is the optimal convergence rate for estimating the policy value regarding the sample size $n$ ($n^{-1/2}$) achievable for FQE under a non-parametric model with a fixed horizon ($T$)? (2) How does the error bound depend on the horizon $T$? (3) What is the role of the probability ratio function in improving the convergence of FQE estimators? Specifically, we show that under the completeness assumption of $Q$-functions, which is mild in the non-parametric setting, the estimation errors for policy value using both parametric and non-parametric FQE estimators can achieve an optimal rate in terms of $n$. The corresponding error bounds in terms of both $n$ and $T$ are also established. With an additional realizability assumption on ratio functions, the rate of estimation errors can be improved from $T^{1.5}/\sqrt{n}$ to $T/\sqrt{n}$, which matches the sharpest known bound in the current literature under the tabular setting.

Electron-neutrino charged-current interactions with xenon nuclei were modeled in the nEXO neutrinoless double-beta decay detector (~5-tonne, 90% ${}^{136}$Xe, 10% ${}^{134}$Xe) to evaluate its sensitivity to supernova neutrinos. Predictions for event rates and detectable signatures were modeled using the MARLEY event generator. We find good agreement between MARLEY's predictions and existing theoretical calculations of the inclusive cross sections at supernova neutrino energies. The interactions modeled by MARLEY were simulated within the nEXO simulation framework and were run through an example reconstruction algorithm to determine the detector's efficiency for reconstructing these events. The simulated data, incorporating the detector response, were used to study the ability of nEXO to reconstruct the incident electron-neutrino spectrum and these results were extended to a larger xenon detector of the same isotope enrichment. We estimate that nEXO will be able to observe electron-neutrino interactions with xenon from supernovae as far as 5 to 8 kpc from earth, while the ability to reconstruct incident electron-neutrino spectrum parameters from observed interactions in nEXO is limited to closer supernovae., Comment: 17 pages, 16 figures

Artificial Intelligence has outperformed human experts in functional tasks such as chess and baduk. How about creative tasks? This paper evaluates AI's capability in the creative domain compared to human experts, which little research has been conducted so far. We propose a novel Prompt-for-Prompt to generate social media creatives via prompt augmentation by Large Language Models. We take the most popular Instagram posts (with the biggest number of like clicks) in top brands' Instagram accounts to create social media creatives. We give GPT 4 several prompt instructions with text descriptions to generate the most effective prompts for cutting-edge text-to-image generators: Midjourney, DALL E 3, and Stable Diffusion. LLM-augmented prompts can boost AI's abilities by adding objectives, engagement strategy, lighting and brand consistency for social media image creation. We conduct an extensive human evaluation experiment, and find that AI excels human experts, and Midjourney is better than the other text-to-image generators. Surprisingly, unlike conventional wisdom in the social media industry, prompt instruction including eye-catching shows much poorer performance than those including natural. Regarding the type of creatives, AI improves creatives with animals or products but less with real people. Also, AI improves creatives with short text descriptions more than with long text descriptions, because there is more room for AI to augment prompts with shorter descriptions., Comment: 17 pages, 5 figures

Covariate balancing methods have been widely applied to single or monotone missing patterns and have certain advantages over likelihood-based methods and inverse probability weighting approaches based on standard logistic regression. In this paper, we consider non-monotone missing data under the complete-case missing variable condition (CCMV), which is a case of missing not at random (MNAR). Using relationships between each missing pattern and the complete-case subsample, a weighted estimator can be used for estimation, where the weight is a sum of ratios of conditional probability of observing a particular missing pattern versus that of observing the complete-case pattern, given the variables observed in the corresponding missing pattern. Plug-in estimators of the propensity ratios, however, can be unbounded and lead to unstable estimation. Using further relations between propensity ratios and balancing of moments across missing patterns, we employ tailored loss functions each encouraging empirical balance across patterns to estimate propensity ratios flexibly using functional basis expansion. We propose two penalizations to separately control propensity ratio model complexity and covariate imbalance. We study the asymptotic properties of the proposed estimators and show that they are consistent under mild smoothness assumptions. Asymptotic normality and efficiency are also developed. Numerical simulation results show that the proposed method achieves smaller mean squared errors than other methods.

We study distributional off-policy evaluation (OPE), of which the goal is to learn the distribution of the return for a target policy using offline data generated by a different policy. The theoretical foundation of many existing work relies on the supremum-extended statistical distances such as supremum-Wasserstein distance, which are hard to estimate. In contrast, we study the more manageable expectation-extended statistical distances and provide a novel theoretical justification on their validity for learning the return distribution. Based on this attractive property, we propose a new method called Energy Bellman Residual Minimizer (EBRM) for distributional OPE. We provide corresponding in-depth theoretical analyses. We establish a finite-sample error bound for the EBRM estimator under the realizability assumption. Furthermore, we introduce a variant of our method based on a multi-step extension which improves the error bound for non-realizable settings. Notably, unlike prior distributional OPE methods, the theoretical guarantees of our method do not require the completeness assumption.

Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles. To enhance interpretability, our model involves a low-dimensional causal embedded space such that all the relevant causal information in the multivariate functional data is preserved in this lower-dimensional subspace. We prove that the proposed model is causally identifiable under standard assumptions that are often made in the causal discovery literature. To carry out inference of our model, we develop a fully Bayesian framework with suitable prior specifications and uncertainty quantification through posterior summaries. We illustrate the superior performance of our method over existing methods in terms of causal graph estimation through extensive simulation studies. We also demonstrate the proposed method using a brain EEG dataset., Comment: 36 pages, 2 figures, 7 tables

The prediction of tropical rain rates from atmospheric profiles poses significant challenges, mainly due to the heavy-tailed distribution exhibited by tropical rainfall. This study introduces over-parameterized neural networks not only to forecast tropical rain rates, but also to explain their heavy-tailed distribution. The prediction is separately conducted for three rain types (stratiform, deep convective, and shallow convective) observed by the Global Precipitation Measurement satellite radar over the West and East Pacific regions. Atmospheric profiles of humidity, temperature, and zonal and meridional winds from the MERRA-2 reanalysis are considered as features. Although over-parameterized neural networks are well-known for their ``double descent phenomenon," little has been explored about their applicability to climate data and capability of capturing the tail behavior of data. In our results, over-parameterized neural networks accurately predict the rain rate distributions and outperform other machine learning methods. Spatial maps show that over-parameterized neural networks also successfully describe spatial patterns of each rain type across the tropical Pacific. In addition, we assess the feature importance for each over-parameterized neural network to provide insight into the key factors driving the predictions, with low-level humidity and temperature variables being the overall most important. These findings highlight the capability of over-parameterized neural networks in predicting the distribution of the rain rate and explaining extreme values.

We study treatment effect estimation with functional treatments where the average potential outcome functional is a function of functions, in contrast to continuous treatment effect estimation where the target is a function of real numbers. By considering a flexible scalar-on-function marginal structural model, a weight-modified kernel ridge regression (WMKRR) is adopted for estimation. The weights are constructed by directly minimizing the uniform balancing error resulting from a decomposition of the WMKRR estimator, instead of being estimated under a particular treatment selection model. Despite the complex structure of the uniform balancing error derived under WMKRR, finite-dimensional convex algorithms can be applied to efficiently solve for the proposed weights thanks to a representer theorem. The optimal convergence rate is shown to be attainable by the proposed WMKRR estimator without any smoothness assumption on the true weight function. Corresponding empirical performance is demonstrated by a simulation study and a real data application.

Periodontitis and Inflammatory Bowel Disease (IBD) are chronic inflammatory conditions, characterized by microbial dysbiosis and hyper-immunoinflammatory responses. Growing evidence suggest an interconnection between periodontitis and IBD, implying a shift from the traditional concept of independent diseases to a complex, reciprocal cycle. This review outlines the evidence supporting an Oral-Gut axis, marked by a higher prevalence of periodontitis in IBD patients and vice versa. The specific mechanisms linking periodontitis and IBD remain to be fully elucidated, but emerging evidence points to the ectopic colonization of the gut by oral bacteria, which promote intestinal inflammation by activating host immune responses. This review presents an in-depth examination of the interconnection between periodontitis and IBD, highlighting the shared microbiological and immunological pathways, and proposing a multi-hit hypothesis in the pathogenesis of periodontitis-mediated intestinal inflammation. Furthermore, the review underscores the critical need for a collaborative approach between dentists and gastroenterologists to provide holistic oral-systemic healthcare., Comment: Total Words: 7,016 Figures: 3 Tables: 2 Reference: 341

Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with unknown shapes and discontinuous jumps on the boundaries. Moreover, the relationship between the response and the tensor covariates can be nonlinear. In this article, we develop a nonlinear Bayesian tensor additive regression model to accommodate such spatial structure. A functional fused elastic net prior is proposed over the additive component functions to comprehensively model the nonlinearity and spatial smoothness, detect the discontinuous jumps, and simultaneously identify the active regions. The great flexibility and interpretability of the proposed method against the alternatives are demonstrated by a simulation study and an analysis on facial feature data.

We study the implicit regularization of gradient descent towards structured sparsity via a novel neural reparameterization, which we call a diagonally grouped linear neural network. We show the following intriguing property of our reparameterization: gradient descent over the squared regression loss, without any explicit regularization, biases towards solutions with a group sparsity structure. In contrast to many existing works in understanding implicit regularization, we prove that our training trajectory cannot be simulated by mirror descent. We analyze the gradient dynamics of the corresponding regression problem in the general noise setting and obtain minimax-optimal error rates. Compared to existing bounds for implicit sparse regularization using diagonal linear networks, our analysis with the new reparameterization shows improved sample complexity. In the degenerate case of size-one groups, our approach gives rise to a new algorithm for sparse linear regression. Finally, we demonstrate the efficacy of our approach with several numerical experiments., Comment: accepted by ICLR 2023

Liquid xenon time projection chambers are promising detectors to search for neutrinoless double beta decay (0$\nu \beta \beta$), due to their response uniformity, monolithic sensitive volume, scalability to large target masses, and suitability for extremely low background operations. The nEXO collaboration has designed a tonne-scale time projection chamber that aims to search for 0$\nu \beta \beta$ of \ce{^{136}Xe} with projected half-life sensitivity of $1.35\times 10^{28}$~yr. To reach this sensitivity, the design goal for nEXO is $\leq$1\% energy resolution at the decay $Q$-value ($2458.07\pm 0.31$~keV). Reaching this resolution requires the efficient collection of both the ionization and scintillation produced in the detector. The nEXO design employs Silicon Photo-Multipliers (SiPMs) to detect the vacuum ultra-violet, 175 nm scintillation light of liquid xenon. This paper reports on the characterization of the newest vacuum ultra-violet sensitive Fondazione Bruno Kessler VUVHD3 SiPMs specifically designed for nEXO, as well as new measurements on new test samples of previously characterised Hamamatsu VUV4 Multi Pixel Photon Counters (MPPCs). Various SiPM and MPPC parameters, such as dark noise, gain, direct crosstalk, correlated avalanches and photon detection efficiency were measured as a function of the applied over voltage and wavelength at liquid xenon temperature (163~K). The results from this study are used to provide updated estimates of the achievable energy resolution at the decay $Q$-value for the nEXO design.

The prevalence of data collected on the same set of samples from multiple sources (i.e., multi-view data) has prompted significant development of data integration methods based on low-rank matrix factorizations. These methods decompose signal matrices from each view into the sum of shared and individual structures, which are further used for dimension reduction, exploratory analyses, and quantifying associations across views. However, existing methods have limitations in modeling partially-shared structures due to either too restrictive models, or restrictive identifiability conditions. To address these challenges, we formulate a new model for partially-shared signals based on grouping the views into so-called hierarchical levels. The proposed hierarchy leads us to introduce a new penalty, hierarchical nuclear norm (HNN), for signal estimation. In contrast to existing methods, HNN penalization avoids scores and loadings factorization of the signals and leads to a convex optimization problem, which we solve using a dual forward-backward algorithm. We propose a simple refitting procedure to adjust the penalization bias and develop an adapted version of bi-cross-validation for selecting tuning parameters. Extensive simulation studies and analysis of the genotype-tissue expression data demonstrate the advantages of our method over existing alternatives., Comment: 39 pages, 10 figures, 3 tables

In the signal processing and statistics literature, the minimum description length (MDL) principle is a popular tool for choosing model complexity. Successful examples include signal denoising and variable selection in linear regression, for which the corresponding MDL solutions often enjoy consistent properties and produce very promising empirical results. This paper demonstrates that MDL can be extended naturally to the high-dimensional setting, where the number of predictors $p$ is larger than the number of observations $n$. It first considers the case of linear regression, then allows for outliers in the data, and lastly extends to the robust fitting of nonparametric additive models. Results from numerical experiments are presented to demonstrate the efficiency and effectiveness of the MDL approach.

We study a possible calibration technique for the nEXO experiment using a $^{127}$Xe electron capture source. nEXO is a next-generation search for neutrinoless double beta decay ($0\nu\beta\beta$) that will use a 5-tonne, monolithic liquid xenon time projection chamber (TPC). The xenon, used both as source and detection medium, will be enriched to 90% in $^{136}$Xe. To optimize the event reconstruction and energy resolution, calibrations are needed to map the position- and time-dependent detector response. The 36.3 day half-life of $^{127}$Xe and its small $Q$-value compared to that of $^{136}$Xe $0\nu\beta\beta$ would allow a small activity to be maintained continuously in the detector during normal operations without introducing additional backgrounds, thereby enabling in-situ calibration and monitoring of the detector response. In this work we describe a process for producing the source and preliminary experimental tests. We then use simulations to project the precision with which such a source could calibrate spatial corrections to the light and charge response of the nEXO TPC., Comment: 24 pages, 16 figures

Understanding how matter behaves at the highest densities and temperatures is a major open problem in both nuclear physics and relativistic astrophysics. This physics is often encapsulated in the so-called high-temperature nuclear equation of state, which influences compact binary mergers, core-collapse supernovae, and many more phenomena. One such case is the type (either black hole or neutron star) and mass of the remnant of the core collapse of a massive star. For each of six candidate equations of state, we use a very large suite of spherically symmetric supernova models to generate a suite of synthetic populations of such remnants. We then compare these synthetic populations to the observed remnant population. We thus provide a novel constraint on the high-temperature nuclear equation of state and describe which EOS candidates are more or less favored by this metric., Comment: Accepted by ApJ Letters; revised version; 3 figures, 2 tables

Offline policy evaluation (OPE) is considered a fundamental and challenging problem in reinforcement learning (RL). This paper focuses on the value estimation of a target policy based on pre-collected data generated from a possibly different policy, under the framework of infinite-horizon Markov decision processes. Motivated by the recently developed marginal importance sampling method in RL and the covariate balancing idea in causal inference, we propose a novel estimator with approximately projected state-action balancing weights for the policy value estimation. We obtain the convergence rate of these weights and show that the proposed value estimator is semi-parametric efficient under technical conditions. In terms of asymptotics, our results scale with both the number of trajectories and the number of decision points at each trajectory. As such, consistency can still be achieved with a limited number of subjects when the number of decision points diverges. In addition, we develop a necessary and sufficient condition for establishing the well-posedness of the Bellman operator in the off-policy setting, which characterizes the difficulty of OPE and may be of independent interest. Numerical experiments demonstrate the promising performance of our proposed estimator.

In this paper, we study the implicit bias of gradient descent for sparse regression. We extend results on regression with quadratic parametrization, which amounts to depth-2 diagonal linear networks, to more general depth-N networks, under more realistic settings of noise and correlated designs. We show that early stopping is crucial for gradient descent to converge to a sparse model, a phenomenon that we call implicit sparse regularization. This result is in sharp contrast to known results for noiseless and uncorrelated-design cases. We characterize the impact of depth and early stopping and show that for a general depth parameter N, gradient descent with early stopping achieves minimax optimal sparse recovery with sufficiently small initialization and step size. In particular, we show that increasing depth enlarges the scale of working initialization and the early-stopping window so that this implicit sparse regularization effect is more likely to take place., Comment: 32 pages, accepted by NeurIPS 2021. arXiv admin note: text overlap with arXiv:1909.05122 by other authors

In this paper, we report on the photon emission of Silicon Photomultipliers (SiPMs) from avalanche pulses generated in dark condition, with the main objective of better understanding the associated systematics for next-generation, large area, SiPM-based physics experiments. A new apparatus for spectral and imaging analysis was developed at TRIUMF and used to measure the light emitted by the two SiPMs considered as photo-sensor candidates for the nEXO neutrinoless double-beta decay experiment: one Fondazione Bruno Kessler (FBK) VUV-HD Low Field (LF) Low After Pulse (Low AP) (VUV-HD3) SiPM, and one Hamamatsu Photonics K.K. (HPK) VUV4 Multi-Pixel Photon Counter (MPPC). Spectral measurements of their light emission were taken with varying over-voltage in the wavelength range of 450--1020\,nm. For the FBK VUV-HD3, at an over-voltage of $12.1\pm1.0$\,V, we measure a secondary photon yield (number of photons ($\gamma$) emitted per charge carrier ($e^{-}$)) of $(4.04\pm0.02)\times 10^{-6}$ $\gamma/e^{-}$. The emission spectrum of the FBK VUV-HD3 contains an interference pattern consistent with thin-film interference. Additionally, emission microscopy images (EMMIs) of the FBK VUV-HD3 show a small number of highly localized regions with increased light intensity (hotspots) randomly distributed over the SiPM surface area. For the HPK VUV4 MPPC, at an over-voltage of $10.7\pm1.0$\,V, we measure a secondary photon yield of $(8.71\pm0.04)\times 10^{-6}$ $\gamma/e^{-}$. In contrast to the FBK VUV-HD3, the emission spectra of the HPK VUV4 don't show an interference pattern -- most likely due to a thinner surface coating. EMMIs of the HPK VUV4 also reveal a larger number of hotspots compared to the FBK VUV-HD3, especially in one of the corners of the device., Comment: 14 pages, 8 figures

In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in the empirical risk without explicitly modeling the observation probabilities, and can be computed efficiently via convex optimization. The recovered matrix based on the proposed weighted empirical risk enjoys appealing theoretical guarantees. In particular, the proposed method achieves a stronger guarantee than existing work in terms of the scaling with respect to the observation probabilities, under asymptotically heterogeneous missing settings (where entry-wise observation probabilities can be of different orders). These settings can be regarded as a better theoretical model of missing patterns with highly varying probabilities. We also provide a new minimax lower bound under a class of heterogeneous settings. Numerical experiments are also provided to demonstrate the effectiveness of the proposed method., Comment: Proceedings of the 38th International Conference on Machine Learning, PMLR 139, 2021

We study nonparametric estimation for the partially conditional average treatment effect, defined as the treatment effect function over an interested subset of confounders. We propose a hybrid kernel weighting estimator where the weights aim to control the balancing error of any function of the confounders from a reproducing kernel Hilbert space after kernel smoothing over the subset of interested variables. In addition, we present an augmented version of our estimator which can incorporate estimations of outcome mean functions. Based on the representer theorem, gradient-based algorithms can be applied for solving the corresponding infinite-dimensional optimization problem. Asymptotic properties are studied without any smoothness assumptions for propensity score function or the need of data splitting, relaxing certain existing stringent assumptions. The numerical performance of the proposed estimator is demonstrated by a simulation study and an application to the effect of a mother's smoking on a baby's birth weight conditioned on the mother's age., Comment: 19 pages, 2 figures

The $\beta$-decay of neutron-rich $^{129}$In into $^{129}$Sn was studied using the GRIFFIN spectrometer at the ISAC facility at TRIUMF. The study observed the half-lives of the ground state and each of the $\beta$-decaying isomers. The level scheme of $^{129}$Sn has been expanded with thirty-one new $\gamma$-ray transitions and nine new excited levels, leading to a re-evaluation of the $\beta$-branching ratios and level spin assignments. The observation of the $\beta$-decay of the (29/2$^{+}$) 1911-keV isomeric state in $^{129}$In is reported for the first time, with a branching ratio of 2.0(5)$\%$.

The $^{80}$Ge structure was investigated in a high-statistics $\beta$-decay experiment of $^{80}$Ga using the GRIFFIN spectrometer at TRIUMF-ISAC through $\gamma$, $\beta$-$e$, $e$-$\gamma$ and $\gamma$-$\gamma$ spectroscopy. No evidence was found for the recently reported 0$_2^{+}$ 639-keV level suggested as evidence for low-energy shape coexistence in $^{80}$Ge. Large-scale shell model calculations performed in $^{78,80,82}$Ge place the $0^{+}_{2}$ level in $^{80}$Ge at 2\,MeV. The new experimental evidence combined with shell model predictions indicate that low-energy shape coexistence is not present in $^{80}$Ge.

Tensor linear regression is an important and useful tool for analyzing tensor data. To deal with high dimensionality, CANDECOMP/PARAFAC (CP) low-rank constraints are often imposed on the coefficient tensor parameter in the (penalized) $M$-estimation. However, we show that the corresponding optimization may not be attainable, and when this happens, the estimator is not well-defined. This is closely related to a phenomenon, called CP degeneracy, in low-rank tensor approximation problems. In this article, we provide useful results of CP degeneracy in tensor regression problems. In addition, we provide a general penalized strategy as a solution to overcome CP degeneracy. The asymptotic properties of the resulting estimation are also studied. Numerical experiments are conducted to illustrate our findings.

Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification, while a model-free method only provides a correlation measure which is inadequate to test independence. In this paper, we adopt the Hilbert-Schmidt Independence Criterion (HSIC) to measure the dependency between two random functions. We develop a two-step procedure by first pre-smoothing each function based on its discrete and noisy measurements and then applying the HSIC to recovered functions. To ensure the compatibility between the two steps such that the effect of the pre-smoothing error on the subsequent HSIC is asymptotically negligible, we propose to use wavelet soft-thresholding for pre-smoothing and Besov-norm-induced kernels for HSIC. We also provide the corresponding asymptotic analysis. The superior numerical performance of the proposed method over existing ones is demonstrated in a simulation study. Moreover, in an magnetoencephalography (MEG) data application, the functional connectivity patterns identified by the proposed method are more anatomically interpretable than those by existing methods.

We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation yields a desirable convergence rate. We also provide a minimax lower bound, which characterizes the optimality of the proposed estimator for a wide range of scenarios. Numerical experiments are conducted to confirm the theoretical findings, and they show that the proposed model has advantages over its existing linear counterparts.

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation approach under the framework of reproducing kernel Hilbert spaces (RKHS) that can handle both sparse and dense functional data. We extend multilinear rank structures for (finite-dimensional) tensors to functions, which allow for flexible modeling of both covariance operators and marginal structures. The proposed framework can guarantee that the resulting estimator is automatically semi-positive definite, and can incorporate various spectral regularizations. The trace-norm regularization in particular can promote low ranks for both covariance operator and marginal structures. Despite the lack of a closed form, under mild assumptions, the proposed estimator can achieve unified theoretical results that hold for any relative magnitudes between the sample size and the number of observations per sample field, and the rate of convergence reveals the "phase-transition" phenomenon from sparse to dense functional data. Based on a new representer theorem, an ADMM algorithm is developed for the trace-norm regularization. The appealing numerical performance of the proposed estimator is demonstrated by a simulation study and the analysis of a dataset from the Argo project., Comment: 25 pages, 4 figures

The low-lying structure of semi-magic $^{118}$Sn has been investigated through the $\beta$-decay of $^{118}$In ($T_{1/2}=4.45$ min) to study shape coexistence via the reduced transition probabilities of states in the 2p-2h proton intruder band. This high-statistics study was carried out at TRIUMF-ISAC with the GRIFFIN spectrometer. In total, 99 transitions have been placed in the level scheme with 43 being newly observed. Three low-lying $\gamma$-ray transitions with energies near 285 keV have been resolved from which the 2$^+_{\mathrm{intr.}} \rightarrow 0^+_{\mathrm{intr.}}$ 284.52-keV transition was determined to have half of the previous branching fraction leading to a $B(E2;2^+_2\rightarrow 0^+_2)$ of 21(4) W.u. compared to 39(7) W.u. from the previous measurement. Calculations using $sd$ IBM-2 with mixing have also been made to compare the experimental $B(E2)$ values to the theoretical values and to make comparisons to the $^{114,116}$Sn isotopes previously studied using the same theoretical model.

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge for large-scale data sets which are increasingly common among matrix completion problems. A simple solution to large-scale problems is parallel computing. However, embarrassingly parallel fashion often leads to inefficient estimators. Based on the idea of pseudo data, we propose a novel refinement step, which turns such inefficient estimators into a rate (near-)optimal matrix completion procedure. The refined estimator is an approximation of a regularized least median estimator, and therefore not an ordinary regularized empirical risk estimator. This leads to a non-standard analysis of asymptotic behaviors. Empirical results are also provided to confirm the effectiveness of the proposed method., Comment: 26 pages, 1 figure, 5 tables

A remarkable recent discovery in machine learning has been that deep neural networks can achieve impressive performance (in terms of both lower training error and higher generalization capacity) in the regime where they are massively over-parameterized. Consequently, over the past year, the community has devoted growing interest in analyzing optimization and generalization properties of over-parameterized networks, and several breakthrough works have led to important theoretical progress. However, the majority of existing work only applies to supervised learning scenarios and hence are limited to settings such as classification and regression. In contrast, the role of over-parameterization in the unsupervised setting has gained far less attention. In this paper, we study the gradient dynamics of two-layer over-parameterized autoencoders with ReLU activation. We make very few assumptions about the given training dataset (other than mild non-degeneracy conditions). Starting from a randomly initialized autoencoder network, we rigorously prove the linear convergence of gradient descent in two learning regimes, namely: (i) the weakly-trained regime where only the encoder is trained, and (ii) the jointly-trained regime where both the encoder and the decoder are trained. Our results indicate the considerable benefits of joint training over weak training for finding global optima, achieving a dramatic decrease in the required level of over-parameterization. We also analyze the case of weight-tied autoencoders (which is a commonly used architectural choice in practical settings) and prove that in the over-parameterized setting, training such networks from randomly initialized points leads to certain unexpected degeneracies., Comment: Added Sections 3.2 and 3.4 on inductive biases. Fixed an error in deriving the neural tangent kernel in Section 3.3

This paper investigates the problem of adjusting for spatial effects in genomic prediction. Despite being seldomly considered in genomic prediction, spatial effects often affect phenotypic measurements of plants. We consider a Gaussian random field model with an additive covariance structure that incorporates genotype effects, spatial effects and subpopulation effects. An empirical study shows the existence of spatial effects and heterogeneity across different subpopulation families, while simulations illustrate the improvement in selecting genotypically superior plants by adjusting for spatial effects in genomic prediction., Comment: 22 pages, 6 figures, 10 tables

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study matrix completion from corrupted data under a novel low-rank missing mechanism. The probability matrix of observation is estimated via a high dimensional low-rank matrix estimation procedure, and further used to complete the target matrix via inverse probabilities weighting. Due to both high dimensional and extreme (i.e., very small) nature of the true probability matrix, the effect of inverse probability weighting requires careful study. We derive optimal asymptotic convergence rates of the proposed estimators for both the observation probabilities and the target matrix., Comment: 29 pages, 0 figures

Gamma-Ray Infrastructure For Fundamental Investigations of Nuclei, GRIFFIN, is a new high-efficiency $\gamma$-ray spectrometer designed for use in decay spectroscopy experiments with low-energy radioactive ion beams provided by TRIUMF's Isotope Separator and Accelerator (ISAC-I) facility. GRIFFIN is composed of sixteen Compton-suppressed large-volume clover-type high-purity germanium (HPGe) $\gamma$-ray detectors combined with a suite of ancillary detection systems and coupled to a custom digital data acquisition system. The infrastructure and detectors of the spectrometer as well as the performance characteristics and the analysis techniques applied to the experimental data are described.

Estimating the probabilities of linkages in a network has gained increasing interest in recent years. One popular model for network analysis is the exchangeable graph model (ExGM) characterized by a two-dimensional function known as a graphon. Estimating an underlying graphon becomes the key of such analysis. Several nonparametric estimation methods have been proposed, and some are provably consistent. However, if certain useful features of the nodes (e.g., age and schools in social network context) are available, none of these methods was designed to incorporate this source of information to help with the estimation. This paper develops a consistent graphon estimation method that integrates the information from both the adjacency matrix itself and node features. We show that properly leveraging the features can improve the estimation. A cross-validation method is proposed to automatically select the tuning parameter of the method.

We provide a series of results for unsupervised learning with autoencoders. Specifically, we study shallow two-layer autoencoder architectures with shared weights. We focus on three generative models for data that are common in statistical machine learning: (i) the mixture-of-gaussians model, (ii) the sparse coding model, and (iii) the sparsity model with non-negative coefficients. For each of these models, we prove that under suitable choices of hyperparameters, architectures, and initialization, autoencoders learned by gradient descent can successfully recover the parameters of the corresponding model. To our knowledge, this is the first result that rigorously studies the dynamics of gradient descent for weight-sharing autoencoders. Our analysis can be viewed as theoretical evidence that shallow autoencoder modules indeed can be used as feature learning mechanisms for a variety of data models, and may shed insight on how to train larger stacked architectures with autoencoders as basic building blocks., Comment: Experimental study on synthesis data added. Typos fixed

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input dataset. However, a key challenge is that storage, transmission, and processing of the learned dictionary can be untenably high if the data dimension is high. In this paper, we consider the double-sparsity model introduced by Rubinstein et al. (2010b) where the dictionary itself is the product of a fixed, known basis and a data-adaptive sparse component. First, we introduce a simple algorithm for double-sparse coding that can be amenable to efficient implementation via neural architectures. Second, we theoretically analyze its performance and demonstrate asymptotic sample complexity and running time benefits over existing (provable) approaches for sparse coding. To our knowledge, our work introduces the first computationally efficient algorithm for double-sparse coding that enjoys rigorous statistical guarantees. Finally, we support our analysis via several numerical experiments on simulated data, confirming that our method can indeed be useful in problem sizes encountered in practical applications., Comment: 40 pages. An abbreviated conference version appears at AAAI 2018

In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper develops a new class of nonparametric covariance function estimators in terms of various spectral regularizations of an operator associated with a reproducing kernel Hilbert space. Despite their nonparametric nature, the covariance estimators are automatically positive semi-definite without any additional modification steps. An unconventional representer theorem is established to provide a finite dimensional representation for this class of covariance estimators, which leads to a closed-form expression of the corresponding $L^2$ eigen-decomposition. Trace-norm regularization is particularly studied to further achieve a low-rank representation, another desirable property which leads to dimension reduction and is often needed in advanced FDA approaches. An efficient algorithm is developed based on the accelerated proximal gradient method. This resulted estimator is shown to enjoy an excellent rate of convergence under both fixed and random designs. The outstanding practical performance of the trace-norm-regularized covariance estimator is demonstrated by a simulation study and the analysis of a traffic dataset., Comment: 26 pages, 3 figures

Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, i.e., sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge this is the first effort to embed change points into a marked Poisson process. Between the change points, the spectrum is modeled non-parametrically using a mixture of a smooth radial basis expansion and a number of local deviations from the smooth term representing spectral emission lines. Because the model is over parameterized we employ an $\ell_1$ penalty. The tuning parameter in the penalty and the number of change points are determined via the minimum description length principle. Our method is validated via a series of simulation studies and its practical utility is illustrated in the analysis of the ultra-fast rotating yellow giant star known as FK Com., Comment: 30 pages, 6 figures

This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This criterion uses the celebrated Huber function from the robust statistics literature to downweigh the effects of outliers. A practical algorithm is developed to solve the optimization involved. This algorithm is fast, straightforward to implement, and monotonic convergent. Furthermore, the proposed methodology is theoretically shown to be stable in a well defined sense. Its promising empirical performance is demonstrated via a sequence of simulation experiments, including image inpainting., Comment: 33 pages, 2 figures

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any discrepancy between the physical reality and the computer model. In an attempt to solve a fundamentally important (but often ignored) identifiability issue between the computer model parameters and the discrepancy function, this paper proposes a new and identifiable parametrization of the calibration problem. It also develops a two-step procedure for estimating all the relevant quantities under the new parameterization. This estimation procedure is shown to enjoy excellent rates of convergence and can be straightforwardly implemented with existing software. For uncertainty quantification, bootstrapping is adopted to construct confidence regions for the quantities of interest. The practical performance of the proposed methodology is illustrated through simulation examples and an application to a computational fluid dynamics model., Comment: 21 pages, 2 figures

Diffusion magnetic resonance imaging is an imaging technology designed to probe anatomical architectures of biological samples in an in vivo and non-invasive manner through measuring water diffusion. The contribution of this paper is threefold. First it proposes a new method to identify and estimate multiple diffusion directions within a voxel through a new and identifiable parametrization of the widely used multi-tensor model. Unlike many existing methods, this method focuses on the estimation of diffusion directions rather than the diffusion tensors. Second, this paper proposes a novel direction smoothing method which greatly improves direction estimation in regions with crossing fibers. This smoothing method is shown to have excellent theoretical and empirical properties. Lastly, this paper develops a fiber tracking algorithm that can handle multiple directions within a voxel. The overall methodology is illustrated with simulated data and a data set collected for the study of Alzheimer's disease by the Alzheimer's Disease Neuroimaging Initiative (ADNI)., Comment: 21 pages, 5 figures

This paper presents a unique learning and research experience for students from mechanical and electrical engineering majors in a course on senior design projects involving research and development, design and production of a proof-of-concept electric vehicle, the ZEM (Zero EMissions) vehicle. The ZEM vehicle combined positive aspects and latest technologies in electric vehicle design,solar-electric power conversions, and ergonomic human power into one affordable and environmentally sustainable vehicle for urban transportation. The 43 mechanical and 10 electrical engineering majors plus 7 students from business participated in this multidisciplinary project spanned over two academic years. The students involved in this multiyear endeavor gained valuable experiences in real-world working environment with multifunctional and multi-year sub-groups. The success of this new attempt in conducting senior design projects classes have set a model for faculty members in the authors' university in conducting similar courses., Comment: Proceedings of Green Energy and Systems Conference 2013, November 25, Long Beach, CA, USA

In astrophysics a common goal is to infer the flux distribution of populations of scientifically interesting objects such as pulsars or supernovae. In practice, inference for the flux distribution is often conducted using the cumulative distribution of the number of sources detected at a given sensitivity. The resulting "$\log(N>S)$-$\log (S)$" relationship can be used to compare and evaluate theoretical models for source populations and their evolution. Under restrictive assumptions the relationship should be linear. In practice, however, when simple theoretical models fail, it is common for astrophysicists to use prespecified piecewise linear models. This paper proposes a methodology for estimating both the number and locations of "breakpoints" in astrophysical source populations that extends beyond existing work in this field. An important component of the proposed methodology is a new interwoven EM algorithm that computes parameter estimates. It is shown that in simple settings such estimates are asymptotically consistent despite the complex nature of the parameter space. Through simulation studies it is demonstrated that the proposed methodology is capable of accurately detecting structural breaks in a variety of parameter configurations. This paper concludes with an application of our methodology to the Chandra Deep Field North (CDFN) data set., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS750 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

A multimethod, multitrait approach was used to examine the relations of aggression and hyperactivity to mastery motivation in preschool children. Parallel measures of multiple facets of mastery motivation were devised from findings in two studies: (study 1) a maternal report questionnaire for 332 twins, ages 3-5, recruited from the twin registry in a Western state; and (study 2) behavioral observations and ratings by trained preschool personnel from the Bethesda Longitudinal Study for 152 normally developing, middle to upper income children during their first 3 years. The findings from both studies indicated that high involvement in and/or vigor at gross motor tasks was associated with high activity, impulsivity, and aggression in preschoolers. Persistence at challenging object-oriented tasks contributed negatively to predicting hyperactivity (Study 1) and impulsivity (Study 2), but did not predict activity level (Study 2), suggesting that the impulsivity aspect of hyperactivity is what is negatively associated with low task persistence. It is argued that, given the high incidence of attention deficit disorders with hyperactivity (ADHD) and aggression in school settings, it is important to study their precursors in preschoolers. Data from the two studies imply that it is important to distinguish between high activity level and hyperactivity, which includes elements of impulsivity and difficulty in maintaining attention to tasks. Teachers may misinterpret social or gross motor mastery attempts, accompanied by high activity level, as ADHD so should be cautioned not to overinterpret what they see. (Contains 11 references.) (KB)

The libraries in U.S. research universities are being systematically depopulated of current subscriptions to scholarly journals. Annual increases in subscription costs are consistently outpacing the growth in library budgets; this has become a chronic problem for academic libraries which collect in the fields of science, engineering, and medicine. Case Western Reserve University has built a novel digital library distribution system and focused collections in the chemical sciences to investigate a new approach to solving a significant portion of this problem. By collaborating with another research library which has a strong chemical sciences collection, they have developed a methodology to control costs of scholarly journals and have planted the seeds of a new consortial model for building digital libraries. This paper summarizes Case Western Reserve University's progress to date and indicates areas in which the University is continuing its research and development. The University's rights management system, consortial and equipment standards, scanning and workflow, and technical justification for a digitization for the consortium are described in appendices. (Author/AEF)

This Technical Research Report gives correlations between student scores on the General Technical (GT) composite of the Armed Services Vocational Aptitude Battery and cumulative grade point averages (GPAs). Data were collected on 911 juniors and seniors selected from a sample at 22 secondary schools in the San Antonio metropolitan area. The GT score was found to significantly relate to overall academic performance for 19 out of the 22 samples, with a median rho of 44. Results indicate that the level of relationship was not differentially affected by school-specific ethnic group composition, school expenditures or average teacher/pupil ratio. Neither the samples used nor conclusions presented in this study should be construed as representative of high schools throughout the country. Since socio-economic levels represented in the various samples go from the highest to the lowest ranges, limited generalizations may be meaningful to other school districts with similar diverse populations. This is an initial report exploring the relationship between student performance on various ASVAB scales and various criteria in the civilian academic sector. Additional studies will further assess relationships across various grade levels, in differing types of training situations, and across different time spans. As such, this first study should be interpreted as a prelude to additional and more comprehensive analyses of the Armed Services Vocational Aptitude Battery. (Author)

This study investigated the interaction of child and parent gender with child responsiveness in determining parents' later selection of discipline. Participants were 40 parents and their preschool children (ten pairs each of mother/daughter, mother/son, father/daughter, and father/son combinations). After being separated from his or her child, each parent was told that the child was assembling a puzzle in an adjacent room and that the parent was to monitor the child's performance telemetrically. The child's successes and errors were indicated by a tone or buzz respectively and were registered on digital counters. The parent was to indicate on console pushbuttons the number of candies (0 to 9) to be added to the child's supply for a success or to be subtracted for an error so that the child would best learn how to do the puzzle. In reality, the child was playing in an adjacent room, and the events that the parent believed were being produced by the child were experimentally manipulated. In baseline, the child appeared to make 50% successes independently of the parent's teaching strategy. Successes then became contingent upon the parent's selection of high, and later low, intensities of punishment for errors. Finally, 100% errors were programmed regardless of parental punishment. Results indicated that the parents' and children's gender and the children's apparent responsiveness to parental discipline combined to determine the parents' administrations of rewarding and punishing consequences for the children's behaviors. (Author/JMB)