In a high dimensional linear predictive regression where the number of potential predictors can be larger than the sample size, we consider using LASSO, a popular L1-penalized regression method, to estimate the sparse coefficients when many unit root regressors are present. Consistency of LASSO relies on two building blocks: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix of the regressors. In our setting where unit root regressors are driven by temporal dependent non-Gaussian innovations, we establish original probabilistic bounds for these two building blocks. The bounds imply that the rates of convergence of LASSO are different from those in the familiar cross sectional case. In practical applications given a mixture of stationary and nonstationary predictors, asymptotic guarantee of LASSO is preserved if all predictors are scale-standardized. In an empirical example of forecasting the unemployment rate with many macroeconomic time series, strong performance is delivered by LASSO when the initial specification is guided by macroeconomic domain expertise.

This work builds on the models and concepts presented in part 1 to learn approximate dictionary representations of Koopman operators from data. Part I of this paper presented a methodology for arguing the subspace invariance of a Koopman dictionary. This methodology was demonstrated on the state-inclusive logistic lifting (SILL) basis. This is an affine basis augmented with conjunctive logistic functions. The SILL dictionary's nonlinear functions are homogeneous, a norm in data-driven dictionary learning of Koopman operators. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm. We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves the same accuracy and dimensional scaling as deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

In this work, we propose a novel generative model for mapping inputs to structured, high-dimensional outputs using structured conditional normalizing flows and Gaussian process regression. The model is motivated by the need to characterize uncertainty in the input/output relationship when making inferences on new data. In particular, in the physical sciences, limited training data may not adequately characterize future observed data; it is critical that models adequately indicate uncertainty, particularly when they may be asked to extrapolate. In our proposed model, structured conditional normalizing flows provide parsimonious latent representations that relate to the inputs through a Gaussian process, providing exact likelihood calculations and uncertainty that naturally increases away from the training data inputs. We demonstrate the methodology on laser-induced breakdown spectroscopy data from the ChemCam instrument onboard the Mars rover Curiosity. ChemCam was designed to recover the chemical composition of rock and soil samples by measuring the spectral properties of plasma atomic emissions induced by a laser pulse. We show that our model can generate realistic spectra conditional on a given chemical composition and that we can use the model to perform uncertainty quantification of chemical compositions for new observed spectra. Based on our results, we anticipate that our proposed modeling approach may be useful in other scientific domains with high-dimensional, complex structure where it is important to quantify predictive uncertainty.

A distribution inference attack aims to infer statistical properties of data used to train machine learning models. These attacks are sometimes surprisingly potent, but the factors that impact distribution inference risk are not well understood and demonstrated attacks often rely on strong and unrealistic assumptions such as full knowledge of training environments even in supposedly black-box threat scenarios. To improve understanding of distribution inference risks, we develop a new black-box attack that even outperforms the best known white-box attack in most settings. Using this new attack, we evaluate distribution inference risk while relaxing a variety of assumptions about the adversary's knowledge under black-box access, like known model architectures and label-only access. Finally, we evaluate the effectiveness of previously proposed defenses and introduce new defenses. We find that although noise-based defenses appear to be ineffective, a simple re-sampling defense can be highly effective. Code is available at https://github.com/iamgroot42/dissecting_distribution_inference

Trajectory-User Linking (TUL) is a relatively new mobility classification task in which anonymous trajectories are linked to the users who generated them. With applications ranging from personalized recommendations to criminal activity detection, TUL has received increasing attention over the past five years. While research has focused mainly on learning deep representations that capture complex spatio-temporal mobility patterns unique to individual users, we demonstrate that visit patterns are highly unique among users and thus simple heuristics applied directly to the raw data are sufficient to solve TUL. More specifically, we demonstrate that a single check-in per trajectory is enough to correctly predict the identity of the user up to 85% of the time. Moreover, by using a non-parametric classifier, we scale up TUL to over 100k users which is an increase over state-of-the-art by three orders of magnitude. Extensive empirical analysis on four real-world datasets (Brightkite, Foursquare, Gowalla and Weeplaces) compares our findings to state-of-the-art results, and more importantly validates our claim that TUL is easier than commonly believed.

Gaussian process state-space model (GPSSM) is a fully probabilistic state-space model that has attracted much attention over the past decade. However, the outputs of the transition function in the existing GPSSMs are assumed to be independent, meaning that the GPSSMs cannot exploit the inductive biases between different outputs and lose certain model capacities. To address this issue, this paper proposes an output-dependent and more realistic GPSSM by utilizing the well-known, simple yet practical linear model of coregionalization (LMC) framework to represent the output dependency. To jointly learn the output-dependent GPSSM and infer the latent states, we propose a variational sparse GP-based learning method that only gently increases the computational complexity. Experiments on both synthetic and real datasets demonstrate the superiority of the output-dependent GPSSM in terms of learning and inference performance.

In this paper, we explore the relationship between an individual's writing style and the risk that they will engage in online harmful behaviors (such as cyberbullying). In particular, we consider whether measurable differences in writing style relate to different personality types, as modeled by the Big-Five personality traits and the Dark Triad traits, and can differentiate between users who do or do not engage in harmful behaviors. We study messages from nearly 2,500 users from two online communities (Twitter and Reddit) and find that we can measure significant personality differences between regular and harmful users from the writing style of as few as 100 tweets or 40 Reddit posts, aggregate these values to distinguish between healthy and harmful communities, and also use style attributes to predict which users will engage in harmful behaviors.

Recent development in the field of explainable artificial intelligence (XAI) has helped improve trust in Machine-Learning-as-a-Service (MLaaS) systems, in which an explanation is provided together with the model prediction in response to each query. However, XAI also opens a door for adversaries to gain insights into the black-box models in MLaaS, thereby making the models more vulnerable to several attacks. For example, feature-based explanations (e.g., SHAP) could expose the top important features that a black-box model focuses on. Such disclosure has been exploited to craft effective backdoor triggers against malware classifiers. To address this trade-off, we introduce a new concept of achieving local differential privacy (LDP) in the explanations, and from that we establish a defense, called XRand, against such attacks. We show that our mechanism restricts the information that the adversary can learn about the top important features, while maintaining the faithfulness of the explanations.

We study the problem of sharing as many branching conditions of a given forest classifier or regressor as possible while keeping classification performance. As a constraint for preventing from accuracy degradation, we first consider the one that the decision paths of all the given feature vectors must not change. For a branching condition that a value of a certain feature is at most a given threshold, the set of values satisfying such constraint can be represented as an interval. Thus, the problem is reduced to the problem of finding the minimum set intersecting all the constraint-satisfying intervals for each set of branching conditions on the same feature. We propose an algorithm for the original problem using an algorithm solving this problem efficiently. The constraint is relaxed later to promote further sharing of branching conditions by allowing decision path change of a certain ratio of the given feature vectors or allowing a certain number of non-intersected constraint-satisfying intervals. We also extended our algorithm for both the relaxations. The effectiveness of our method is demonstrated through comprehensive experiments using 21 datasets (13 classification and 8 regression datasets in UCI machine learning repository) and 4 classifiers/regressors (random forest, extremely randomized trees, AdaBoost and gradient boosting).

Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and responses $\mathcal{Y}$ are both high-dimensional tensors. By demonstrating that the general inner product or the contracted product on a unit rank tensor can be decomposed into standard inner products and outer products, the problem can be simply transformed into a tensor to scalar regression followed by a tensor decomposition. So we propose a fast solution based on stagewise search composed by contraction part and generation part which are optimized alternatively. We successfully demonstrate our method can out perform current methods in terms of accuracy and predictors selection by effectively incorporating the structural information.