Understanding implicit bias of gradient descent has been an important goal in machine learning research. Unfortunately, even for a single-neuron ReLU network, it recently proved impossible to characterize the implicit regularization with the square loss by an explicit function of the norm of model parameters. In order to close the gap between the existing theory and the intriguing empirical behavior of ReLU networks, here we examine the gradient flow dynamics in the parameter space when training single-neuron ReLU networks. Specifically, we discover implicit bias in terms of support vectors in ReLU networks, which play a key role in why and how ReLU networks generalize well. Moreover, we analyze gradient flows with respect to the magnitude of the norm of initialization, and show the impact of the norm in gradient dynamics. Lastly, under some conditions, we prove that the norm of the learned weight strictly increases on the gradient flow.

Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined with a $\ell_1$ sparsity regularizer. However, most of the existing methods suffer from slow convergence performance caused by the {\em double} non-smooth objective. To accelerate the computation, in this paper, we proposed a decentralized surrogate median regression (deSMR) method for efficiently solving the decentralized sparsity learning problem. We show that our proposed algorithm enjoys a linear convergence rate with a simple implementation. We also investigate the statistical guarantee, and it shows that our proposed estimator achieves a near-oracle convergence rate without any restriction on the number of network nodes. Moreover, we establish the theoretical results for sparse support recovery. Thorough numerical experiments and real data study are provided to demonstrate the effectiveness of our method.

Real data are rarely pure. Hence the past half-century has seen great interest in robust estimation algorithms that perform well even when part of the data is corrupt. However, their vast majority approach optimal accuracy only when given a tight upper bound on the fraction of corrupt data. Such bounds are not available in practice, resulting in weak guarantees and often poor performance. This brief note abstracts the complex and pervasive robustness problem into a simple geometric puzzle. It then applies the puzzle's solution to derive a universal meta technique that converts any robust estimation algorithm requiring a tight corruption-level upper bound to achieve its optimal accuracy into one achieving essentially the same accuracy without using any upper bounds.

Learning data representations under uncertainty is an important task that emerges in numerous machine learning applications. However, uncertainty quantification (UQ) techniques are computationally intensive and become prohibitively expensive for high-dimensional data. In this paper, we present a novel surrogate model for representation learning and uncertainty quantification, which aims to deal with data of moderate to high dimensions. The proposed model combines a neural network approach for dimensionality reduction of the (potentially high-dimensional) data, with a surrogate model method for learning the data distribution. We first employ a variational autoencoder (VAE) to learn a low-dimensional representation of the data distribution. We then propose to harness polynomial chaos expansion (PCE) formulation to map this distribution to the output target. The coefficients of PCE are learned from the distribution representation of the training data using a maximum mean discrepancy (MMD) approach. Our model enables us to (a) learn a representation of the data, (b) estimate uncertainty in the high-dimensional data system, and (c) match high order moments of the output distribution; without any prior statistical assumptions on the data. Numerical experimental results are presented to illustrate the performance of the proposed method.

K-Nearest Neighbor(KNN) algorithm is a poplar model and falls under the Supervised Learning and it can be used to solve both classification and regression problems. In this article, I would be giving you a detailed explanation and how this model works. K-Nearest Neighbor is one of the simplest Machine Learning algorithms based on Supervised Learning technique. KNN algorithm assumes the similarity between the new data and available data and put the new case into the category that is most similar to the available categories. The value of the K is very important.

Events across a timeline are a common data representation, seen in different temporal modalities. Individual atomic events can occur in a certain temporal ordering to compose higher level composite events. Examples of a composite event are a patient's medical symptom or a baseball player hitting a home run, caused distinct temporal orderings of patient vitals and player movements respectively. Such salient composite events are provided as labels in temporal datasets and most works optimize models to predict these composite event labels directly. We focus on uncovering the underlying atomic events and their relations that lead to the composite events within a noisy temporal data setting. We propose Neural Temporal Logic Programming (Neural TLP) which first learns implicit temporal relations between atomic events and then lifts logic rules for composite events, given only the composite events labels for supervision. This is done through efficiently searching through the combinatorial space of all temporal logic rules in an end-to-end differentiable manner. We evaluate our method on video and healthcare datasets where it outperforms the baseline methods for rule discovery.

Federated learning (FL) is capable of performing large distributed machine learning tasks across multiple edge users by periodically aggregating trained local parameters. To address key challenges of enabling FL over a wireless fog-cloud system (e.g., non-i.i.d. data, users' heterogeneity), we first propose an efficient FL algorithm based on Federated Averaging (called FedFog) to perform the local aggregation of gradient parameters at fog servers and global training update at the cloud. Next, we employ FedFog in wireless fog-cloud systems by investigating a novel network-aware FL optimization problem that strikes the balance between the global loss and completion time. An iterative algorithm is then developed to obtain a precise measurement of the system performance, which helps design an efficient stopping criteria to output an appropriate number of global rounds. To mitigate the straggler effect, we propose a flexible user aggregation strategy that trains fast users first to obtain a certain level of accuracy before allowing slow users to join the global training updates. Extensive numerical results using several real-world FL tasks are provided to verify the theoretical convergence of FedFog. We also show that the proposed co-design of FL and communication is essential to substantially improve resource utilization while achieving comparable accuracy of the learning model.

Moderators and automated methods enforce bans on malicious users who engage in disruptive behavior. However, malicious users can easily create a new account to evade such bans. Previous research has focused on other forms of online deception, like the simultaneous operation of multiple accounts by the same entities (sockpuppetry), impersonation of other individuals, and studying the effects of de-platforming individuals and communities. Here we conduct the first data-driven study of ban evasion, i.e., the act of circumventing bans on an online platform, leading to temporally disjoint operation of accounts by the same user. We curate a novel dataset of 8,551 ban evasion pairs (parent, child) identified on Wikipedia and contrast their behavior with benign users and non-evading malicious users. We find that evasion child accounts demonstrate similarities with respect to their banned parent accounts on several behavioral axes - from similarity in usernames and edited pages to similarity in content added to the platform and its psycholinguistic attributes. We reveal key behavioral attributes of accounts that are likely to evade bans. Based on the insights from the analyses, we train logistic regression classifiers to detect and predict ban evasion at three different points in the ban evasion lifecycle. Results demonstrate the effectiveness of our methods in predicting future evaders (AUC = 0.78), early detection of ban evasion (AUC = 0.85), and matching child accounts with parent accounts (MRR = 0.97). Our work can aid moderators by reducing their workload and identifying evasion pairs faster and more efficiently than current manual and heuristic-based approaches. Dataset is available https://github.com/srijankr/ban_evasion.

The earth observation industry provides satellite imagery with high spatial resolution and short revisit time. To allow efficient operational employment of these images, automating certain tasks has become necessary. In the defense domain, aircraft detection on satellite imagery is a valuable tool for analysts. Obtaining high performance detectors on such a task can only be achieved by leveraging deep learning and thus us-ing a large amount of labeled data. To obtain labels of a high enough quality, the knowledge of military experts is needed.We propose a hybrid clustering active learning method to select the most relevant data to label, thus limiting the amount of data required and further improving the performances. It combines diversity- and uncertainty-based active learning selection methods. For aircraft detection by segmentation, we show that this method can provide better or competitive results compared to other active learning methods.

In this paper, we consider learning scenarios where the learned model is evaluated under an unknown test distribution which potentially differs from the training distribution (i.e. distribution shift). The learner has access to a family of weight functions such that the test distribution is a reweighting of the training distribution under one of these functions, a setting typically studied under the name of Distributionally Robust Optimization (DRO). We consider the problem of deriving regret bounds in the classical learning theory setting, and require that the resulting regret bounds hold uniformly for all potential test distributions. We show that the DRO formulation does not guarantee uniformly small regret under distribution shift. We instead propose an alternative method called Minimax Regret Optimization (MRO), and show that under suitable conditions this method achieves uniformly low regret across all test distributions. We also adapt our technique to have stronger guarantees when the test distributions are heterogeneous in their similarity to the training data. Given the widespead optimization of worst case risks in current approaches to robust machine learning, we believe that MRO can be a strong alternative to address distribution shift scenarios.