Community detection is one of the most important methodological fields of network science, and one which has attracted a significant amount of attention over the past decades. This area deals with the automated division of a network into fundamental building blocks, with the objective of providing a summary of its large-scale structure. Despite its importance and widespread adoption, there is a noticeable gap between what is considered the state-of-the-art and the methods that are actually used in practice in a variety of fields. Here we attempt to address this discrepancy by dividing existing methods according to whether they have a "descriptive" or an "inferential" goal. While descriptive methods find patterns in networks based on intuitive notions of community structure, inferential methods articulate a precise generative model, and attempt to fit it to data. In this way, they are able to provide insights into the mechanisms of network formation, and separate structure from randomness in a manner supported by statistical evidence. We review how employing descriptive methods with inferential aims is riddled with pitfalls and misleading answers, and thus should be in general avoided. We argue that inferential methods are more typically aligned with clearer scientific questions, yield more robust results, and should be in many cases preferred. We attempt to dispel some myths and half-truths often believed when community detection is employed in practice, in an effort to improve both the use of such methods as well as the interpretation of their results.

We consider the task of reconstructing polytopes with fixed facet directions from finitely many support function evaluations. We show that for fixed simplicial normal fan the least-squares estimate is given by a convex quadratic program. We study the geometry of the solution set and give a combinatorial characterization for the uniqueness of the reconstruction in this case. We provide an algorithm that, under mild assumptions, converges to the unknown input shape as the number of noisy support function evaluations increases. We also discuss limitations of our results if the restriction on the normal fan is removed.

Risk scores are widely used for clinical decision making and commonly generated from logistic regression models. Machine-learning-based methods may work well for identifying important predictors, but such 'black box' variable selection limits interpretability, and variable importance evaluated from a single model can be biased. We propose a robust and interpretable variable selection approach using the recently developed Shapley variable importance cloud (ShapleyVIC) that accounts for variability across models. Our approach evaluates and visualizes overall variable contributions for in-depth inference and transparent variable selection, and filters out non-significant contributors to simplify model building steps. We derive an ensemble variable ranking from variable contributions, which is easily integrated with an automated and modularized risk score generator, AutoScore, for convenient implementation. In a study of early death or unplanned readmission, ShapleyVIC selected 6 of 41 candidate variables to create a well-performing model, which had similar performance to a 16-variable model from machine-learning-based ranking.

This work aims to address the long-established problem of learning diversified representations. To this end, we combine information-theoretic arguments with stochastic competition-based activations, namely Stochastic Local Winner-Takes-All (LWTA) units. In this context, we ditch the conventional deep architectures commonly used in Representation Learning, that rely on non-linear activations; instead, we replace them with sets of locally and stochastically competing linear units. In this setting, each network layer yields sparse outputs, determined by the outcome of the competition between units that are organized into blocks of competitors. We adopt stochastic arguments for the competition mechanism, which perform posterior sampling to determine the winner of each block. We further endow the considered networks with the ability to infer the sub-part of the network that is essential for modeling the data at hand; we impose appropriate stick-breaking priors to this end. To further enrich the information of the emerging representations, we resort to information-theoretic principles, namely the Information Competing Process (ICP). Then, all the components are tied together under the stochastic Variational Bayes framework for inference. We perform a thorough experimental investigation for our approach using benchmark datasets on image classification. As we experimentally show, the resulting networks yield significant discriminative representation learning abilities. In addition, the introduced paradigm allows for a principled investigation mechanism of the emerging intermediate network representations.

Suppose that we have a regression problem with response variable Y in $\mathbb{R}^d$ and predictor X in $\mathbb{R}^d$, for $d \geq 1$. In permuted or unlinked regression we have access to separate unordered data on X and Y, as opposed to data on (X,Y)-pairs in usual regression. So far in the literature the case $d=1$ has received attention, see e.g., the recent papers by Rigollet and Weed [Information & Inference, 8, 619--717] and Balabdaoui et al. [J. Mach. Learn. Res., 22(172), 1--60]. In this paper, we consider the general multivariate setting with $d \geq 1$. We show that the notion of cyclical monotonicity of the regression function is sufficient for identification and estimation in the permuted/unlinked regression model. We study permutation recovery in the permuted regression setting and develop a computationally efficient and easy-to-use algorithm for denoising based on the Kiefer-Wolfowitz [Ann. Math. Statist., 27, 887--906] nonparametric maximum likelihood estimator and techniques from the theory of optimal transport. We provide explicit upper bounds on the associated mean squared denoising error for Gaussian noise. As in previous work on the case $d = 1$, the permuted/unlinked setting involves slow (logarithmic) rates of convergence rooting in the underlying deconvolution problem. Numerical studies corroborate our theoretical analysis and show that the proposed approach performs at least on par with the methods in the aforementioned prior work in the case $d = 1$ while achieving substantial reductions in terms of computational complexity.

We study the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) with heavy-tailed data. Specifically, we focus on the $\ell_1$-norm linear regression in the $\epsilon$-DP model. While most of the previous work focuses on the case where the loss function is Lipschitz, here we only need to assume the variates has bounded moments. Firstly, we study the case where the $\ell_2$ norm of data has bounded second order moment. We propose an algorithm which is based on the exponential mechanism and show that it is possible to achieve an upper bound of $\tilde{O}(\sqrt{\frac{d}{n\epsilon}})$ (with high probability). Next, we relax the assumption to bounded $\theta$-th order moment with some $\theta\in (1, 2)$ and show that it is possible to achieve an upper bound of $\tilde{O}(({\frac{d}{n\epsilon}})^\frac{\theta-1}{\theta})$. Our algorithms can also be extended to more relaxed cases where only each coordinate of the data has bounded moments, and we can get an upper bound of $\tilde{O}({\frac{d}{\sqrt{n\epsilon}}})$ and $\tilde{O}({\frac{d}{({n\epsilon})^\frac{\theta-1}{\theta}}})$ in the second and $\theta$-th moment case respectively.

There has been a surge of interest in developing robust estimators for models with heavy-tailed data in statistics and machine learning. This paper proposes a log-truncated M-estimator for a large family of statistical regressions and establishes its excess risk bound under the condition that the data have $(1+\varepsilon)$-th moment with $\varepsilon \in (0,1]$. With an additional assumption on the associated risk function, we obtain an $\ell_2$-error bound for the estimation. Our theorems are applied to establish robust M-estimators for concrete regressions. Besides convex regressions such as quantile regression and generalized linear models, many non-convex regressions can also be fit into our theorems, we focus on robust deep neural network regressions, which can be solved by the stochastic gradient descent algorithms. Simulations and real data analysis demonstrate the superiority of log-truncated estimations over standard estimations.

Currently, publicly available models for website classification do not offer an embedding method and have limited support for languages beyond English. We release a dataset with more than 1M websites in 92 languages with relative labels collected from Curlie, the largest multilingual crowdsourced Web directory. The dataset contains 14 website categories aligned across languages. Alongside it, we introduce Homepage2Vec, a machine-learned pre-trained model for classifying and embedding websites based on their homepage in a language-agnostic way. Homepage2Vec, thanks to its feature set (textual content, metadata tags, and visual attributes) and recent progress in natural language representation, is language-independent by design and can generate embeddings representation. We show that Homepage2Vec correctly classifies websites with a macro-averaged F1-score of 0.90, with stable performance across low- as well as high-resource languages. Feature analysis shows that a small subset of efficiently computable features suffices to achieve high performance even with limited computational resources. We make publicly available the curated Curlie dataset aligned across languages, the pre-trained Homepage2Vec model, and libraries.

Fair machine learning aims to mitigate the biases of model predictions against certain subpopulations regarding sensitive attributes such as race and gender. Among the many existing fairness notions, counterfactual fairness measures the model fairness from a causal perspective by comparing the predictions of each individual from the original data and the counterfactuals. In counterfactuals, the sensitive attribute values of this individual had been modified. Recently, a few works extend counterfactual fairness to graph data, but most of them neglect the following facts that can lead to biases: 1) the sensitive attributes of each node's neighbors may causally affect the prediction w.r.t. this node; 2) the sensitive attributes may causally affect other features and the graph structure. To tackle these issues, in this paper, we propose a novel fairness notion - graph counterfactual fairness, which considers the biases led by the above facts. To learn node representations towards graph counterfactual fairness, we propose a novel framework based on counterfactual data augmentation. In this framework, we generate counterfactuals corresponding to perturbations on each node's and their neighbors' sensitive attributes. Then we enforce fairness by minimizing the discrepancy between the representations learned from the original graph and the counterfactuals for each node. Experiments on both synthetic and real-world graphs show that our framework outperforms the state-of-the-art baselines in graph counterfactual fairness, and also achieves comparable prediction performance.

Extremely large pre-trained language models (PTMs) such as GPT-3 are usually released as a service, allowing users to design task-specific prompts to query the PTMs through some black-box APIs. In such a scenario, which we call Language-Model-as-a-Service (LMaaS), gradients of the PTMs are usually not available. Can we optimize the task prompts by only accessing the model inference APIs? Based on recent observations that large PTMs have a very low intrinsic dimensionality, this work proposes the Black-Box Tuning to optimize PTMs through derivative-free algorithms. In particular, we invoke the CMA-ES to optimize the continuous prompt prepended to the input text by iteratively calling PTM inference APIs. Our experimental results demonstrate that, black-box tuning with RoBERTa on a few labeled samples not only significantly outperforms manual prompt and GPT-3's in-context learning, but also surpasses the gradient-based counterparts, namely prompt tuning and full model tuning.