Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the conditional distribution of outputs given the inputs is a key object. The input dependent conditional distribution of an output can be encoded with an RKHS valued function, the conditional kernel mean map. In this paper we present a new recursive algorithm to estimate the conditional kernel mean map in a Hilbert space valued $L_2$ space, that is in a Bochner space. We prove the weak and strong $L_2$ consistency of our recursive estimator under mild conditions. The idea is to generalize Stone's theorem for Hilbert space valued regression in a locally compact Polish space. We present new insights about conditional kernel mean embeddings and give strong asymptotic bounds regarding the convergence of the proposed recursive method. Finally, the results are demonstrated on three application domains: for inputs coming from Euclidean spaces, Riemannian manifolds and locally compact subsets of function spaces.

Twitter bot detection has become an increasingly important task to combat misinformation, facilitate social media moderation, and preserve the integrity of the online discourse. State-of-the-art bot detection methods generally leverage the graph structure of the Twitter network, and they exhibit promising performance when confronting novel Twitter bots that traditional methods fail to detect. However, very few of the existing Twitter bot detection datasets are graph-based, and even these few graph-based datasets suffer from limited dataset scale, incomplete graph structure, as well as low annotation quality. In fact, the lack of a large-scale graph-based Twitter bot detection benchmark that addresses these issues has seriously hindered the development and evaluation of novel graph-based bot detection approaches. In this paper, we propose TwiBot-22, a comprehensive graph-based Twitter bot detection benchmark that presents the largest dataset to date, provides diversified entities and relations on the Twitter network, and has considerably better annotation quality than existing datasets. In addition, we re-implement 35 representative Twitter bot detection baselines and evaluate them on 9 datasets, including TwiBot-22, to promote a fair comparison of model performance and a holistic understanding of research progress. To facilitate further research, we consolidate all implemented codes and datasets into the TwiBot-22 evaluation framework, where researchers could consistently evaluate new models and datasets. The TwiBot-22 Twitter bot detection benchmark and evaluation framework are publicly available at https://twibot22.github.io/.

Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained problems or constrained upper-level problems. This paper considers the stochastic bilevel optimization problems with equality constraints both in the upper and lower levels. By leveraging the special structure of the equality constraints problem, the paper first presents an alternating implicit projected SGD approach and establishes the $\tilde{\cal O}(\epsilon^{-2})$ sample complexity that matches the state-of-the-art complexity of ALSET \citep{chen2021closing} for unconstrained bilevel problems. To further save the cost of projection, the paper presents two alternating implicit projection-efficient SGD approaches, where one algorithm enjoys the $\tilde{\cal O}(\epsilon^{-2}/T)$ upper-level and $\tilde{\cal O}(\epsilon^{-1.5}/T^{\frac{3}{4}})$ lower-level projection complexity with ${\cal O}(T)$ lower-level batch size, and the other one enjoys $\tilde{\cal O}(\epsilon^{-1.5})$ upper-level and lower-level projection complexity with ${\cal O}(1)$ batch size. Application to federated bilevel optimization has been presented to showcase the empirical performance of our algorithms. Our results demonstrate that equality-constrained bilevel optimization with strongly-convex lower-level problems can be solved as efficiently as stochastic single-level optimization problems.

We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chan et al. (2016) provided a new model of trend inflation with linear inequality constraints on the stochastic trend. We implemented the proposed quadratic programming-based method for this model and compared it to the existing approximation. We observed that the proposed method works as well as the existing approximation in terms of the final trend estimates while achieving gains in terms of sample efficiency.

Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn), has been developed to overcome these limitations. NNetEn entropy is computed using a modified LogNNet neural network classification model. The algorithm contains a reservoir matrix of N=19625 elements that must be filled with the given data. The contribution of this paper is threefold. Firstly, this work investigates different methods of filling the reservoir with time series (signal) elements. The reservoir filling method determines the accuracy of the entropy estimation by convolution of the study time series and LogNNet test data. The present study proposes 6 methods for filling the reservoir for time series. Two of them (Method 3 and Method 6) employ the novel approach of stretching the time series to create intermediate elements that complement it, but do not change its dynamics. The most reliable methods for short time series are Method 3 and Method 5. The second part of the study examines the influence of noise and constant bias on entropy values. Our study examines three different time series data types (chaotic, periodic, and binary) with different dynamic properties, Signal to Noise Ratio (SNR), and offsets. The NNetEn entropy calculation errors are less than 10% when SNR is greater than 30 dB, and entropy decreases with an increase in the bias component. The third part of the article analyzes real-time biosignal EEG data collected from emotion recognition experiments. The NNetEn measures show robustness under low-amplitude noise using various filters. Thus, NNetEn measures entropy effectively when applied to real-world environments with ambient noise, white noise, and 1/f noise.

One of the primary goals in spectrum occupancy mapping is to create a system that is robust to assumptions about the number of sensors, occupancy threshold (in dBm), sensor noise, number of emitters and the propagation environment. We show that such a system may be designed with neural networks using a process of aggregation to allow a variable number of sensors during training and testing. This process transforms the variable number of measurements into approximate log-likelihood ratios (LLRs), which are fed as a fixed-resolution image into a neural network. The use of LLR's provides robustness to the effects of noise and occupancy threshold. In other words, a system may be trained for a nominal number of sensors, threshold and noise levels, and still operate well at various other levels without retraining. Our system operates without knowledge of the number of emitters and does not explicitly attempt to estimate their number or power. Receiver operating curves with realistic propagation environments using topographic maps with commercial network design tools show how performance of the neural network varies with the environment. The use of very low-resolution sensors in this system can still yield good performance. Manuscript received: February 14, 2023.

Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the literature. However, most of the studies require the input dimension to be fixed and consequently ignore the effect of dimension on the rate of convergence and hamper their applications to modern big data with high dimensionality. In this paper, we bridge this gap by analyzing a $k^{th}$ order nonparametric interaction model in both growing dimension scenarios ($d$ grows with $n$ but at a slower rate) and in high dimension ($d \gtrsim n$). In the latter case, sparsity assumptions and associated regularization are required in order to obtain optimal rates of convergence. A new challenge in diverging dimension setting is in calculation mean-square error, the covariance terms among estimated additive components are an order of magnitude larger than those of the variances and they can deteriorate statistical properties without proper care. We introduce a critical debiasing technique to amend the problem. We show that under certain standard assumptions, debiased deep neural networks achieve a minimax optimal rate both in terms of $(n, d)$. Our proof techniques rely crucially on a novel debiasing technique that makes the covariances of additive components negligible in the mean-square error calculation. In addition, we establish the matching lower bounds.

The importance of neighborhood construction in local explanation methods has been already highlighted in the literature. And several attempts have been made to improve neighborhood quality for high-dimensional data, for example, texts, by adopting generative models. Although the generators produce more realistic samples, the intuitive sampling approaches in the existing solutions leave the latent space underexplored. To overcome this problem, our work, focusing on local model-agnostic explanations for text classifiers, proposes a progressive approximation approach that refines the neighborhood of a to-be-explained decision with a careful two-stage interpolation using counterfactuals as landmarks. We explicitly specify the two properties that should be satisfied by generative models, the reconstruction ability and the locality-preserving property, to guide the selection of generators for local explanation methods. Moreover, noticing the opacity of generative models during the study, we propose another method that implements progressive neighborhood approximation with probability-based editions as an alternative to the generator-based solution. The explanation results from both methods consist of word-level and instance-level explanations benefiting from the realistic neighborhood. Through exhaustive experiments, we qualitatively and quantitatively demonstrate the effectiveness of the two proposed methods.

The use of algorithms for decision-making in higher education is steadily growing, promising cost-savings to institutions and personalized service for students but also raising ethical challenges around surveillance, fairness, and interpretation of data. To address the lack of systematic understanding of how these algorithms are currently designed, we reviewed an extensive corpus of papers proposing algorithms for decision-making in higher education. We categorized them based on input data, computational method, and target outcome, and then investigated the interrelations of these factors with the application of human-centered lenses: theoretical, participatory, or speculative design. We found that the models are trending towards deep learning, and increased use of student personal data and protected attributes, with the target scope expanding towards automated decisions. However, despite the associated decrease in interpretability and explainability, current development predominantly fails to incorporate human-centered lenses. We discuss the challenges with these trends and advocate for a human-centered approach.

Collaboration between healthcare institutions can significantly lessen the imbalance in medical resources across various geographic areas. However, directly sharing diagnostic information between institutions is typically not permitted due to the protection of patients' highly sensitive privacy. As a novel privacy-preserving machine learning paradigm, federated learning (FL) makes it possible to maximize the data utility among multiple medical institutions. These feature-enrichment FL techniques are referred to as vertical FL (VFL). Traditional VFL can only benefit multi-parties' shared samples, which strongly restricts its application scope. In order to improve the information-sharing capability and innovation of various healthcare-related institutions, and then to establish a next-generation open medical collaboration network, we propose a unified framework for vertical federated knowledge transfer mechanism (VFedTrans) based on a novel cross-hospital representation distillation component. Specifically, our framework includes three steps. First, shared samples' federated representations are extracted by collaboratively modeling multi-parties' joint features with current efficient vertical federated representation learning methods. Second, for each hospital, we learn a local-representation-distilled module, which can transfer the knowledge from shared samples' federated representations to enrich local samples' representations. Finally, each hospital can leverage local samples' representations enriched by the distillation module to boost arbitrary downstream machine learning tasks. The experiments on real-life medical datasets verify the knowledge transfer effectiveness of our framework.