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Anomaly detection among a large number of processes arises in many applications ranging from dynamic spectrum access to cybersecurity. In such problems one can often obtain noisy observations aggregated from a chosen subset of processes that conforms to a tree structure. The distribution of these observations, based on which the presence of anomalies is detected, may be only partially known. This gives rise to the need for a search strategy designed to account for both the sample complexity and the detection accuracy, as well as cope with statistical models that are known only up to some missing parameters. In this work we propose a sequential search strategy using two variations of the Generalized Local Likelihood Ratio statistic. Our proposed Hierarchical Dynamic Search (HDS) strategy is shown to be order-optimal with respect to the size of the search space and asymptotically optimal with respect to the detection accuracy. An explicit upper bound on the error probability of HDS is established for the finite sample regime. Extensive experiments are conducted, demonstrating the performance gains of HDS over existing methods.

Distributed machine learning (ML) can bring more computational resources to bear than single-machine learning, thus enabling reductions in training time. Distributed learning partitions models and data over many machines, allowing model and dataset sizes beyond the available compute power and memory of a single machine. In practice though, distributed ML is challenging when distribution is mandatory, rather than chosen by the practitioner. In such scenarios, data could unavoidably be separated among workers due to limited memory capacity per worker or even because of data privacy issues. There, existing distributed methods will utterly fail due to dominant transfer costs across workers, or do not even apply. We propose a new approach to distributed fully connected neural network learning, called independent subnet training (IST), to handle these cases. In IST, the original network is decomposed into a set of narrow subnetworks with the same depth. These subnetworks are then trained locally before parameters are exchanged to produce new subnets and the training cycle repeats. Such a naturally "model parallel" approach limits memory usage by storing only a portion of network parameters on each device. Additionally, no requirements exist for sharing data between workers (i.e., subnet training is local and independent) and communication volume and frequency are reduced by decomposing the original network into independent subnets. These properties of IST can cope with issues due to distributed data, slow interconnects, or limited device memory, making IST a suitable approach for cases of mandatory distribution. We show experimentally that IST results in training times that are much lower than common distributed learning approaches.

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the \emph{distribution-free} testing model. Here, the distance between functions is measured with respect to an unknown distribution $\mathcal{D}$ over $\mathbb{R}^n$ from which we can draw samples. In contrast to previous work, we do not assume that $\mathcal{D}$ has finite support. We design a tester that given query access to $f$, and sample access to $\mathcal{D}$, makes $(d/\varepsilon)^{O(1)}$ many queries to $f$, accepts with probability $1$ if $f$ is a polynomial of degree $d$, and rejects with probability at least $2/3$ if every degree-$d$ polynomial $P$ disagrees with $f$ on a set of mass at least $\varepsilon$ with respect to $\mathcal{D}$. Our result also holds under mild assumptions when we receive only a polynomial number of bits of precision for each query to $f$, or when $f$ can only be queried on rational points representable using a logarithmic number of bits. Along the way, we prove a new stability theorem for multivariate polynomials that may be of independent interest.

Policy gradient (PG) estimation becomes a challenge when we are not allowed to sample with the target policy but only have access to a dataset generated by some unknown behavior policy. Conventional methods for off-policy PG estimation often suffer from either significant bias or exponentially large variance. In this paper, we propose the double Fitted PG estimation (FPG) algorithm. FPG can work with an arbitrary policy parameterization, assuming access to a Bellman-complete value function class. In the case of linear value function approximation, we provide a tight finite-sample upper bound on policy gradient estimation error, that is governed by the amount of distribution mismatch measured in feature space. We also establish the asymptotic normality of FPG estimation error with a precise covariance characterization, which is further shown to be statistically optimal with a matching Cramer-Rao lower bound. Empirically, we evaluate the performance of FPG on both policy gradient estimation and policy optimization, using either softmax tabular or ReLU policy networks. Under various metrics, our results show that FPG significantly outperforms existing off-policy PG estimation methods based on importance sampling and variance reduction techniques.

Federated learning with differential privacy, or private federated learning, provides a strategy to train machine learning models while respecting users' privacy. However, differential privacy can disproportionately degrade the performance of the models on under-represented groups, as these parts of the distribution are difficult to learn in the presence of noise. Existing approaches for enforcing fairness in machine learning models have considered the centralized setting, in which the algorithm has access to the users' data. This paper introduces an algorithm to enforce group fairness in private federated learning, where users' data does not leave their devices. First, the paper extends the modified method of differential multipliers to empirical risk minimization with fairness constraints, thus providing an algorithm to enforce fairness in the central setting. Then, this algorithm is extended to the private federated learning setting. The proposed algorithm, \texttt{FPFL}, is tested on a federated version of the Adult dataset and an "unfair" version of the FEMNIST dataset. The experiments on these datasets show how private federated learning accentuates unfairness in the trained models, and how FPFL is able to mitigate such unfairness.

Training a generalizable 3D part segmentation network is quite challenging but of great importance in real-world applications. To tackle this problem, some works design task-specific solutions by translating human understanding of the task to machine's learning process, which faces the risk of missing the optimal strategy since machines do not necessarily understand in the exact human way. Others try to use conventional task-agnostic approaches designed for domain generalization problems with no task prior knowledge considered. To solve the above issues, we propose AutoGPart, a generic method enabling training generalizable 3D part segmentation networks with the task prior considered. AutoGPart builds a supervision space with geometric prior knowledge encoded, and lets the machine to search for the optimal supervisions from the space for a specific segmentation task automatically. Extensive experiments on three generalizable 3D part segmentation tasks are conducted to demonstrate the effectiveness and versatility of AutoGPart. We demonstrate that the performance of segmentation networks using simple backbones can be significantly improved when trained with supervisions searched by our method.

Recognizing human locomotion intent and activities is important for controlling the wearable robots while walking in complex environments. However, human-robot interface signals are usually user-dependent, which causes that the classifier trained on source subjects performs poorly on new subjects. To address this issue, this paper designs the ensemble diverse hypotheses and knowledge distillation (EDHKD) method to realize unsupervised cross-subject adaptation. EDH mitigates the divergence between labeled data of source subjects and unlabeled data of target subjects to accurately classify the locomotion modes of target subjects without labeling data. Compared to previous domain adaptation methods based on the single learner, which may only learn a subset of features from input signals, EDH can learn diverse features by incorporating multiple diverse feature generators and thus increases the accuracy and decreases the variance of classifying target data, but it sacrifices the efficiency. To solve this problem, EDHKD (student) distills the knowledge from the EDH (teacher) to a single network to remain efficient and accurate. The performance of the EDHKD is theoretically proved and experimentally validated on a 2D moon dataset and two public human locomotion datasets. Experimental results show that the EDHKD outperforms all other methods. The EDHKD can classify target data with 96.9%, 94.4%, and 97.4% average accuracy on the above three datasets with a short computing time (1 ms). Compared to a benchmark (BM) method, the EDHKD increases 1.3% and 7.1% average accuracy for classifying the locomotion modes of target subjects. The EDHKD also stabilizes the learning curves. Therefore, the EDHKD is significant for increasing the generalization ability and efficiency of the human intent prediction and human activity recognition system, which will improve human-robot interactions.

There are many important high dimensional function classes that have fast agnostic learning algorithms when strong assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be sufficiently confident that the data indeed satisfies the distributional assumption, so that one can trust in the output quality of the agnostic learning algorithm? We propose a model by which to systematically study the design of tester-learner pairs $(\mathcal{A},\mathcal{T})$, such that if the distribution on examples in the data passes the tester $\mathcal{T}$ then one can safely trust the output of the agnostic learner $\mathcal{A}$ on the data. To demonstrate the power of the model, we apply it to the classical problem of agnostically learning halfspaces under the standard Gaussian distribution and present a tester-learner pair with a combined run-time of $n^{\tilde{O}(1/\epsilon^4)}$. This qualitatively matches that of the best known ordinary agnostic learning algorithms for this task. In contrast, finite sample Gaussian distribution testers do not exist for the $L_1$ and EMD distance measures. A key step in the analysis is a novel characterization of concentration and anti-concentration properties of a distribution whose low-degree moments approximately match those of a Gaussian. We also use tools from polynomial approximation theory. In contrast, we show strong lower bounds on the combined run-times of tester-learner pairs for the problems of agnostically learning convex sets under the Gaussian distribution and for monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Through these lower bounds we exhibit natural problems where there is a dramatic gap between standard agnostic learning run-time and the run-time of the best tester-learner pair.

Proactive dialogue system is able to lead the conversation to a goal topic and has advantaged potential in bargain, persuasion and negotiation. Current corpus-based learning manner limits its practical application in real-world scenarios. To this end, we contribute to advance the study of the proactive dialogue policy to a more natural and challenging setting, i.e., interacting dynamically with users. Further, we call attention to the non-cooperative user behavior -- the user talks about off-path topics when he/she is not satisfied with the previous topics introduced by the agent. We argue that the targets of reaching the goal topic quickly and maintaining a high user satisfaction are not always converge, because the topics close to the goal and the topics user preferred may not be the same. Towards this issue, we propose a new solution named I-Pro that can learn Proactive policy in the Interactive setting. Specifically, we learn the trade-off via a learned goal weight, which consists of four factors (dialogue turn, goal completion difficulty, user satisfaction estimation, and cooperative degree). The experimental results demonstrate I-Pro significantly outperforms baselines in terms of effectiveness and interpretability.