Federated learning (FL) is a distributed learning approach where a set of end-user devices participate in the learning process by acting on their isolated local data sets. Here, we process local data sets of users where worst-case optimization theory is used to reformulate the FL problem where the impact of local data sets in training phase is considered as an uncertain function bounded in a closed uncertainty region. This representation allows us to compare the performance of FL with its centralized counterpart, and to replace the uncertain function with a concept of protection functions leading to more tractable formulation. The latter supports applying a regularization factor in each user cost function in FL to reach a better performance. We evaluated our model using the MNIST data set versus the protection function parameters, e.g., regularization factors.

-- In this paper, we study the fundamental performance limitations for generic feedback systems in which both the controller and the plant may be arbitrarily causal while the disturbance can be with any distributions. We also examine the implications of the generic bounds for machine-learning-in-the-loop control; in other words, fundamental limits in general exist to what machine learning elements in feedback loops can achieve. Machine learning techniques are becoming more and more prevalent nowadays in the feedback control of dynamical systems, where system dynamics that are determined by physical laws will play an indispensable role. In this trend, it is becoming more and more critical to be fully aware of the performance limits of the machine learning algorithms that are to be embedded in the feedback loop, especially in scenarios where performance guarantees are required and must be strictly imposed. In conventional performance limitation analysis [1] of feedback systems such as the Bode integral [2], however, specific restrictions on the classes of the controller that can be implemented must be imposed in general. These restrictions would normally render the analysis invalid if machine learning elements such as deep learning or reinforcement learning are to be placed at the position of the controller, as a result of the complexity of the learning algorithms.

We introduce a novel framework for analysing stationary time series based on optimal transport distances and spectral embeddings. First, we represent time series by their power spectral density (PSD), which summarises the signal energy spread across the Fourier spectrum. Second, we endow the space of PSDs with the Wasserstein distance, which capitalises its unique ability to preserve the geometric information of a set of distributions. These two steps enable us to define the Wasserstein-Fourier (WF) distance, which allows us to compare stationary time series even when they differ in sampling rate, length, magnitude and phase. We analyse the features of WF by blending the properties of the Wasserstein distance and those of the Fourier transform. The proposed WF distance is then used in three sets of key time series applications considering real-world datasets: (i) interpolation of time series leading to data augmentation, (ii) dimensionality reduction via non-linear PCA, and (iii) parametric and non-parametric classification tasks. Our conceptual and experimental findings validate the general concept of using divergences of distributions, especially the Wasserstein distance, to analyse time series through comparing their spectral representations.

We develop a framework for the analysis of deep neural networks and neural ODE models that are trained with stochastic gradient algorithms. We do that by identifying the connections between high-dimensional data-driven control problems, deep learning and theory of statistical sampling. In particular, we derive and study a mean-field (over-damped) Langevin algorithm for solving relaxed data-driven control problems. A key step in the analysis is to derive Pontryagin's optimality principle for data-driven relaxed control problems. Subsequently, we study uniform-in-time propagation of chaos of time-discretised Mean-Field (overdamped) Langevin dynamics. We derive explicit convergence rate in terms of the learning rate, the number of particles/model parameters and the number of iterations of the gradient algorithm. In addition, we study the error arising when using a finite training data set and thus provide quantitive bounds on the generalisation error. Crucially, the obtained rates are dimension-independent. This is possible by exploiting the regularity of the model with respect to the measure over the parameter space (relaxed control).

In mixed multi-view data, multiple sets of diverse features are measured on the same set of samples. By integrating all available data sources, we seek to discover common group structure among the samples that may be hidden in individualistic cluster analyses of a single data-view. While several techniques for such integrative clustering have been explored, we propose and develop a convex formalization that will inherit the strong statistical, mathematical and empirical properties of increasingly popular convex clustering methods. Specifically, our Integrative Generalized Convex Clustering Optimization (iGecco) method employs different convex distances, losses, or divergences for each of the different data views with a joint convex fusion penalty that leads to common groups. Additionally, integrating mixed multi-view data is often challenging when each data source is high-dimensional. To perform feature selection in such scenarios, we develop an adaptive shifted group-lasso penalty that selects features by shrinking them towards their loss-specific centers. Our so-called iGecco+ approach selects features from each data-view that are best for determining the groups, often leading to improved integrative clustering. To fit our model, we develop a new type of generalized multi-block ADMM algorithm using sub-problem approximations that more efficiently fits our model for big data sets. Through a series of numerical experiments and real data examples on text mining and genomics, we show that iGecco+ achieves superior empirical performance for high-dimensional mixed multi-view data.

Self-driving vehicles have expanded dramatically over the last few years. Udacity has release a dataset containing, among other data, a set of images with the steering angle captured during driving. The Udacity challenge aimed to predict steering angle based on only the provided images. W e explore two different models to perform high quality prediction of steering angles based on images using different deep learning techniques including Transfer Learning, 3D CNN, LSTM and ResNet. If the Udacity challenge was still ongoing, both of our models would have placed in the top ten of all entries.

Neural network language models (NNLMs) have achieved ever-improving accuracy due to more sophisticated architectures and increasing amounts of training data. However, the inductive bias of these models (formed by the distributional hypothesis of language), while ideally suited to modeling most running text, results in key limitations for today's models. In particular, the models often struggle to learn certain spatial, temporal, or quantitative relationships, which are commonplace in text and are second-nature for human readers. Yet, in many cases, these relationships can be encoded with simple mathematical or logical expressions. How can we augment today's neural models with such encodings? In this paper, we propose a general methodology to enhance the inductive bias of NNLMs by incorporating simple functions into a neural architecture to form a hierarchical neural-symbolic language model (NSLM). These functions explicitly encode symbolic deterministic relationships to form probability distributions over words. We explore the effectiveness of this approach on numbers and geographic locations, and show that NSLMs significantly reduce perplexity in small-corpus language modeling, and that the performance improvement persists for rare tokens even on much larger corpora. The approach is simple and general, and we discuss how it can be applied to other word classes beyond numbers and geography.

We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a heuristic analysis of a multivariate performance measure called the MMSE matrix. These results show that the combined effects of seemingly very different types of information can be characterized explicitly in terms of formulas involving low-dimensional estimation problems in additive Gaussian noise. Our analysis is supported by numerical simulations.

The objective of this work is to improve the accuracy of building demand forecasting . This is a more challenging t ask than grid level forecasting. For the said purpose, we develop a new technique called recurrent transform learning (RTL). The first one (RTL) is unsupervised; this is used as a feature extraction tool that is further fed into a regression model. Forecasting experiments have been carried out on three popular publicly available datasets. Both of our proposed techniques yield results superior to the state - of - the - art like long short term memory network, echo state network and sparse coding regression. Index Terms -- demand forecasting, dynamical model, load forecasting, transform learning . H E impor tance of electrical load forecasting is well known. The issue has gained even more significance with the advent of smartgrids, microgrids and smart buildings. An excellent review on this topic can be found in [1].

Unsupervised learning of disentangled representations is an open problem in machine learning. The Disentanglement-PyTorch library is developed to facilitate research, implementation, and testing of new variational algorithms. In this modular library, neural architectures, dimensionality of the latent space, and the training algorithms are fully decoupled, allowing for independent and consistent experiments across variational methods. The library handles the training scheduling, logging, and visualizations of reconstructions and latent space traversals. It also evaluates the encodings based on various disentanglement metrics. The library, so far, includes implementations of the following unsupervised algorithms VAE, Beta-VAE, Factor-VAE, DIP-I-VAE, DIP-II-VAE, Info-VAE, and Beta-TCVAE, as well as conditional approaches such as CVAE and IFCVAE. The library is compatible with the Disentanglement Challenge of NeurIPS 2019, hosted on AICrowd, and achieved the 3rd rank in both the first and second stages of the challenge.