On Statistical Efficiency in Learning

A central issue of many statistical learning problems is to select an appropriate model from a set of candidate models. Large models tend to inflate the variance (or overfitting), while small models tend to cause biases (or underfitting) for a given fixed dataset. In this work, we address the critical challenge of model selection to strike a balance between model fitting and model complexity, thus gaining reliable predictive power. We consider the task of approaching the theoretical limit of statistical learning, meaning that the selected model has the predictive performance that is as good as the best possible model given a class of potentially misspecified candidate models. We propose a generalized notion of Takeuchis information criterion and prove that the proposed method can asymptotically achieve the optimal out-sample prediction loss under reasonable assumptions. It is the first proof of the asymptotic property of Takeuchis information criterion to our best knowledge. Our proof applies to a wide variety of nonlinear models, loss functions, and high dimensionality (in the sense that the models complexity can grow with sample size). The proposed method can be used as a computationally efficient surrogate for leave-one-out cross-validation. Moreover, for modeling streaming data, we propose an online algorithm that sequentially expands the model complexity to enhance selection stability and reduce computation cost. Experimental studies show that the proposed method has desirable predictive power and significantly less computational cost than some popular methods.

Automating Botnet Detection with Graph Neural Networks

Botnets are now a major source for many network attacks, such as DDoS attacks and spam. However, most traditional detection methods heavily rely on heuristically designed multi-stage detection criteria. In this paper, we consider the neural network design challenges of using modern deep learning techniques to learn policies for botnet detection automatically. To generate training data, we synthesize botnet connections with different underlying communication patterns overlaid on large-scale real networks as datasets. To capture the important hierarchical structure of centralized botnets and the fast-mixing structure for decentralized botnets, we tailor graph neural networks (GNN) to detect the properties of these structures. Experimental results show that GNNs are better able to capture botnet structure than previous non-learning methods when trained with appropriate data, and that deeper GNNs are crucial for learning difficult botnet topologies. We believe our data and studies can be useful for both the network security and graph learning communities.

Efficiency Limits of Solar Energy Harvesting via Internal Photoemission in Carbon Materials

We describe strategies to estimate the upper limits of the efficiency of photon energy harvesting via hot electron extraction from gapless absorbers. Gapless materials such as noble metals can be used for harvesting the whole solar spectrum, including visible and near-infrared light. The energy of photo-generated non-equilibrium or hot charge carriers can be harvested before they thermalize with the crystal lattice via the process of their internal photo-emission (IPE) through the rectifying Schottky junction with a semiconductor. However, the low efficiency and the high cost of noble metals necessitates the search for cheaper abundant alternative materials, and we show here that carbon can serve as a promising IPE material candidate. We compare the upper limits of performance of IPE photon energy-harvesting platforms, which incorporate either gold or carbon as the photoactive material where hot electrons are generated. Through a combination of density functional theory, joint electron density of states calculations, and Schottky diode efficiency modeling, we show that the material electron band structure imposes a strict upper limit on the achievable efficiency of the IPE devices. Our calculations reveal that graphite is a good material candidate for the IPE absorber for harvesting visible and near-infrared photons. Graphite electron density of states yields a sizeable population of hot electrons with energies high enough to be collected across the potential barrier. We also discuss the mechanisms that prevent the IPE device efficiency from reaching the upper limits imposed by their material electron band structures. The proposed approach is general and allows for efficient pre-screening of materials for their potential use in IPE energy converters and photodetectors within application-specific spectral windows.

Phonon Hydrodynamic Heat Conduction and Knudsen Minimum in Graphite

In the hydrodynamic regime, phonons drift with a nonzero collective velocity under a temperature gradient, reminiscent of viscous gas and fluid flow. The study of hydrodynamic phonon transport has spanned over half a century but has been mostly limited to cryogenic temperatures (~1 K) and more recently to low-dimensional materials. Here, we identify graphite as a three-dimensional material that supports phonon hydrodynamics at significantly higher temperatures (~100 K) based on first-principles calculations. In particular, by solving the Boltzmann equation for phonon transport in graphite ribbons, we predict that phonon Poiseuille flow and Knudsen minimum can be experimentally observed above liquid nitrogen temperature. Further, we reveal the microscopic origin of these intriguing phenomena in terms of the dependence of the effective boundary scattering rate on momentum-conserving phonon-phonon scattering processes and the collective motion of phonons. The significant hydrodynamic nature of phonon transport in graphite is attributed to its strong intralayer sp2 hybrid bonding and weak van der Waals interlayer interactions. As a boundary-sensitive transport regime, phonon hydrodynamics opens up new possibilities for thermal management and energy conversion.

$textit{Ab initio}$ study of electron mean free paths and thermoelectric properties of lead telluride

Last few years have witnessed significant enhancement of thermoelectric figure of merit of lead telluride (PbTe) via nanostructuring. Despite the experimental progress, current understanding of the electron transport in PbTe is based on either band structure calculation using first principles with constant relaxation time approximation or empirical models, both relying on adjustable parameters obtained by fitting experimental data. Here, we report parameter-free first-principles calculation of electron and phonon transport properties of PbTe, including mode-by-mode electron-phonon scattering analysis, leading to detailed information on electron mean free paths and the contributions of electrons and phonons with different mean free paths to thermoelectric transport properties in PbTe. Such information will help to rationalize the use and optimization of nanosctructures to achieve high thermoelectric figure of merit.

The Effect of Shallow vs. Deep Level Doping on the Performance of Thermoelectric Materials

It is well known that the efficiency of a good thermoelectric material should be optimized with respect to doping concentration. However, much less attention has been paid to the optimization of the dopants energy level. Thermoelectric materials doped with shallow levels may experience a dramatic reduction in their figures of merit at high temperatures due to the excitation of minority carriers that reduces the Seebeck coefficient and increases bipolar heat conduction. Doping with deep level impurities can delay the excitation of minority carriers as it requires a higher temperature to ionize all dopants. We find through modeling that, depending on the material type and temperature range of operation, different impurity levels (shallow or deep) will be desired to optimize the efficiency of a thermoelectric material. For different materials, we further clarify where the most preferable position of the impurity level within the band gap falls. Our research provides insights in choosing the most appropriate dopants for a thermoelectric material in order to maximize the device efficiency.