Federated Learning (FL) enables learning a shared model across many clients without violating the privacy requirements. One of the key attributes in FL is the heterogeneity that exists in both resource and data due to the differences in computation and communication capacity, as well as the quantity and content of data among different clients. We conduct a case study to show that heterogeneity in resource and data has a significant impact on training time and model accuracy in conventional FL systems. To this end, we propose TiFL, a Tier-based Federated Learning System, which divides clients into tiers based on their training performance and selects clients from the same tier in each training round to mitigate the straggler problem caused by heterogeneity in resource and data quantity. To further tame the heterogeneity caused by non-IID (Independent and Identical Distribution) data and resources, TiFL employs an adaptive tier selection approach to update the tiering on-the-fly based on the observed training performance and accuracy overtime. We prototype TiFL in a FL testbed following Google's FL architecture and evaluate it using popular benchmarks and the state-of-the-art FL benchmark LEAF. Experimental evaluation shows that TiFL outperforms the conventional FL in various heterogeneous conditions. With the proposed adaptive tier selection policy, we demonstrate that TiFL achieves much faster training performance while keeping the same (and in some cases - better) test accuracy across the board.

A fundamental problem in statistics and machine learning is that of using observed data to predict future observations. This is particularly challenging for model-based approaches because often the goal is to carry out this prediction with no or minimal model assumptions. For example, the inferential model (IM) approach is attractive because it has certain validity guarantees, but requires specification of a parametric model. Here we show that a new perspective on a recently developed generalized IM approach can be applied to construct an IM for prediction that satisfies the desirable validity guarantees without specification of a model. One important special case of this approach corresponds to the powerful conformal prediction framework and, consequently, the desirable properties of conformal prediction follow immediately from the general IM validity theory. Several numerical examples are presented to illustrate the theory and highlight the method's performance and flexibility.

An online resource scheduling framework is proposed for minimizing the sum of weighted task latency for all the mobile users, by optimizing offloading decision, transmission power, and resource allocation in the mobile edge computing (MEC) system. Towards this end, a deep reinforcement learning (DRL) method is proposed to obtain an online resource scheduling policy. Firstly, a related and regularized stacked auto encoder (2r-SAE) with unsupervised learning is proposed to perform data compression and representation for high dimensional channel quality information (CQI) data, which can reduce the state space for DRL. Secondly, we present an adaptive simulated annealing based approach (ASA) as the action search method of DRL, in which an adaptive h-mutation is used to guide the search direction and an adaptive iteration is proposed to enhance the search efficiency during the DRL process. Thirdly, a preserved and prioritized experience replay (2p-ER) is introduced to assist the DRL to train the policy network and find the optimal offloading policy. Numerical results are provided to demonstrate that the proposed algorithm can achieve near-optimal performance while significantly decreasing the computational time compared with existing benchmarks. It also shows that the proposed framework is suitable for resource scheduling problem in large-scale MEC networks, especially in the dynamic environment.

Outlier detection has received special attention in various fields, mainly for those dealing with machine learning and artificial intelligence. As strong outliers, anomalies are divided into the point, contextual and collective outliers. The most important challenges in outlier detection include the thin boundary between the remote points and natural area, the tendency of new data and noise to mimic the real data, unlabelled datasets and different definitions for outliers in different applications. Considering the stated challenges, we defined new types of anomalies called Collective Normal Anomaly and Collective Point Anomaly in order to improve a much better detection of the thin boundary between different types of anomalies. Basic domain-independent methods are introduced to detect these defined anomalies in both unsupervised and supervised datasets. The Multi-Layer Perceptron Neural Network is enhanced using the Genetic Algorithm to detect newly defined anomalies with higher precision so as to ensure a test error less than that calculated for the conventional Multi-Layer Perceptron Neural Network. Experimental results on benchmark datasets indicated reduced error of anomaly detection process in comparison to baselines.

We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as if the covariates were fully observed. Recent literature on this subject proposes instead to design a specific, often complicated or non-convex, algorithm tailored to the case of missing covariates. We investigate a simpler approach where we fill-in the missing entries with their conditional mean given the observed covariates. We show that this imputation scheme coupled with standard off-the-shelf procedures such as the LASSO and square-root LASSO retains the minimax estimation rate in the random-design setting where the covariates are i.i.d.\ sub-Gaussian. We further show that the square-root LASSO remains \emph{pivotal} in this setting. It is often the case that the conditional expectation cannot be computed exactly and must be approximated from data. We study two cases where the covariates either follow an autoregressive (AR) process, or are jointly Gaussian with sparse precision matrix. We propose tractable estimators for the conditional expectation and then perform linear regression via LASSO, and show similar estimation rates in both cases. We complement our theoretical results with simulations on synthetic and semi-synthetic examples, illustrating not only the sharpness of our bounds, but also the broader utility of this strategy beyond our theoretical assumptions.

How can we ensure that a machine learning system produces an o utput that generalizes to the underlying distribution, rather than overfitting its train ing data? That is, how can we ensure that the hypotheses or models that are produced are reflective of t he underlying population the training data was drawn from, rather than patterns that occur only by c hance in the training data? This is perhaps the fundamental question for the science of statist ical machine learning. A vast array of methods have been proposed to answer this ques tion. Most notably, the theory of uniform convergence shows that, if the output is sufficiently "simple," then it cannot overfit too much. A more recent line of work has used distributional stability (in the form of differential privacy) to provide generalization guarantees that compose adaptivel y - that is, statistical validity is preserved even when a dataset is reused multiple times with each succes sive analysis being influenced by the outcomes of prior analyses. Other methods for proving gener alization include compression schemes and uniform stability. Unfortunately, these different methods for providing gener alization guarantees are largely disconnected from one another; it is, in general, not possible t o compare or combine techniques. In this paper, we provide a framework to reason about many of the se these differing approaches using the unifying language of information theory.

Unpaired image-to-image translation has attracted significant interest due to the invention of CycleGAN, a method which utilizes a combination of adversarial and cycle consistency losses to avoid the need for paired data. It is known that the CycleGAN problem might admit multiple solutions, and our goal in this paper is to analyze the space of exact solutions and to give perturbation bounds for approximate solutions. We show theoretically that the exact solution space is invariant with respect to automorphisms of the underlying probability spaces, and, furthermore, that the group of automorphisms acts freely and transitively on the space of exact solutions. We examine the case of zero `pure' CycleGAN loss first in its generality, and, subsequently, expand our analysis to approximate solutions for `extended' CycleGAN loss where identity loss term is included. In order to demonstrate that these results are applicable, we show that under mild conditions nontrivial smooth automorphisms exist. Furthermore, we provide empirical evidence that neural networks can learn these automorphisms with unexpected and unwanted results. We conclude that finding optimal solutions to the CycleGAN loss does not necessarily lead to the envisioned result in image-to-image translation tasks and that underlying hidden symmetries can render the result utterly useless.

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where the equation's geometrically meaningful coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these networks to be designed with built-in symmetries such as rotation equivariance instead of being restricted to just translation equivariance as in traditional CNNs. Having all the desired symmetries included in the design obviates the need to include them by means of costly techniques such as data augmentation. Roto-translation equivariance for image analysis applications is the example we will be using throughout the paper. Our default PDE is solved by a combination of linear group convolutions and non-linear morphological group convolutions. Just like for linear convolution a morphological convolution is specified by a kernel and this kernel is what is being optimized during the training process. We demonstrate how the common CNN operations of max/min-pooling and ReLUs arise naturally from solving a PDE and how they are subsumed by morphological convolutions. We present a proof-of-concept experiment to demonstrate the potential of this framework in increasing the performance of deep learning based imaging applications.

MagNet: Discovering Multi-agent Interaction Dynamics using Neural Network Priyabrata Saha, Arslan Ali, Burhan A. Mudassar, Y un Long and Saibal Mukhopadhyay Abstract -- We present the MagNet, a multi-agent interaction network to discover governing dynamics and predict evolution of a complex system from observations. We formulate a multi-agent system as a coupled nonlinear network with a generic ordinary differential equation (ODE) based state evolution, and develop a neural network based realization of its time-discretized model. MagNet is trained to discover the core dynamics of a multi-agent system from observations, and tuned online to learn agent-specific parameters of the dynamics to ensure accurate prediction even when physical or relational attributes of agents, or number of agents change. We evaluate MagNet on point-mass system in two-dimensional space, Ku-ramoto phase synchronization dynamics and predator-swarm interaction dynamics demonstrating orders of magnitude improvement in prediction accuracy over traditional deep learning models. I NTRODUCTION Multi-agent systems are prevalent in both the natural world and engineered world. Engineered distributed systems of mobile robots, multiple sensors, unmanned aerial vehicles etc. often take inspiration from natural multi-agent systems like swarms, schools, flocks, and herds of social animals or birds. Understanding the behavior of such natural or engineered multi-agent systems from sensory observations is a key challenge in robotics from the design and adversarial perspective. Discovering the hidden dynamics of a multi-agent interaction from observations will enable machines to simulate and predict evolution of complex systems.

In this study we investigate the potential for using Synthetic Aperture Radar (SAR) data to provide high resolution defoliation and regrowth mapping of trees in the tundra-forest ecotone. Using in situ measurements collected in 2017 we calculated the proportion of both live and defoliated tree crown for 165 $10 m \times 10 m$ ground plots along six transects. Quad-polarimetric SAR data from RADARSAT-2 was collected from the same area, and the complex multilook polarimetric covariance matrix was calculated using a novel extension of guided nonlocal means speckle filtering. The nonlocal approach allows us to preserve the high spatial resolution of single-look complex data, which is essential for accurate mapping of the sparsely scattered trees in the study area. Using a standard random forest classification algorithm, our filtering results in a $73.8 \%$ classification accuracy, higher than traditional speckle filtering methods, and on par with the classification accuracy based on optical data.