We analyse the learning performance of Distributed Gradient Descent in the context of multi-agent decentralised non-parametric regression with the square loss function when i.i.d. We show that if agents hold sufficiently many samples with respect to the network size, then Distributed Gradient Descent achieves optimal statistical rates with a number of iterations that scales, up to a threshold, with the inverse of the spectral gap of the gossip matrix divided by the number of samples owned by each agent raised to a problem-dependent power. The presence of the threshold comes from statistics. It encodes the existence of a "big data" regime where the number of required iterations does not depend on the network topology. In this regime, Distributed Gradient Descent achieves optimal statistical rates with the same order of iterations as gradient descent run with all the samples in the network.

Deep neural networks have received dramatic success based on the optimization method of stochastic gradient descent (SGD). However, it is still not clear how to tune hyper-parameters, especially batch size and learning rate, to ensure good generalization. This paper reports both theoretical and empirical evidence of a training strategy that we should control the ratio of batch size to learning rate not too large to achieve a good generalization ability. Specifically, we prove a PAC-Bayes generalization bound for neural networks trained by SGD, which has a positive correlation with the ratio of batch size to learning rate. This correlation builds the theoretical foundation of the training strategy. Furthermore, we conduct a large-scale experiment to verify the correlation and training strategy.

This paper develops a prediction-based prescriptive model for optimal decision making that (i) predicts the outcome under each action using a robust nonlinear model, and (ii) adopts a randomized prescriptive policy determined by the predicted outcomes. The predictive model combines a new regularized regression technique, which was developed using Distributionally Robust Optimization (DRO) with an ambiguity set constructed from the Wasserstein metric, with the K-Nearest Neighbors (K-NN) regression, which helps to capture the nonlinearity embedded in the data. We show theoretical results that guarantee the out-of-sample performance of the predictive model, and prove the optimality of the randomized policy in terms of the expected true future outcome. We demonstrate the proposed methodology on a hypertension dataset, showing that our prescribed treatment leads to a larger reduction in the systolic blood pressure compared to a series of alternatives. A clinically meaningful threshold level used to activate the randomized policy is also derived under a sub-Gaussian assumption on the predicted outcome.

In this paper we propose to use a denoising autoencoder (DAE) prior to simultaneously solve a linear inverse problem and estimate its noise parameter. Existing DAE-based methods estimate the noise parameter empirically or treat it as a tunable hyper-parameter. We instead propose autoencoder guided EM, a probabilistically sound framework that performs Bayesian inference with intractable deep priors. We show that efficient posterior sampling from the DAE can be achieved via Metropolis-Hastings, which allows the Monte Carlo EM algorithm to be used. We demonstrate competitive results for signal denoising, image deblurring and image devignetting.

Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regression coefficients. We investigate the problem of Bayesian linear regression, with the goal of computing posterior distributions that correctly quantify uncertainty given privately released statistics. We show that a naive approach that ignores the noise injected by the privacy mechanism does a poor job in realistic data settings. We then develop noise-aware methods that perform inference over the privacy mechanism and produce correct posteriors across a wide range of scenarios.

Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep learning settings admits a non-Gaussian, heavy-tailed behavior. This suggests that the gradient noise can be modeled by using $\alpha$-stable distributions, a family of heavy-tailed distributions that appear in the generalized central limit theorem. In this context, SGD can be viewed as a discretization of a stochastic differential equation (SDE) driven by a L\'{e}vy motion, and the metastability results for this SDE can then be used for illuminating the behavior of SGD, especially in terms of preferring wide minima'. While this approach brings a new perspective for analyzing SGD, it is limited in the sense that, due to the time discretization, SGD might admit a significantly different behavior than its continuous-time limit.

In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases into training in a hope to reduce statistical complexity. Alternatively, we propose stochastically shared embeddings (SSE), a data-driven approach to regularizing embedding layers, which stochastically transitions between embeddings during stochastic gradient descent (SGD). Because SSE integrates seamlessly with existing SGD algorithms, it can be used with only minor modifications when training large scale neural networks. We develop two versions of SSE: SSE-Graph using knowledge graphs of embeddings; SSE-SE using no prior information.

One important data type which includes time series, digital signals and any sequential observations is still mainly processed with rather standard mathematical and algorithmic routines. In this talk, we will review, what are the main sources of time series in the world, what are the "basic" algorithms and how exactly they might be improved and replaced with different neural network architectures. Apart from the models' details, we will also study the typical tasks that have to be solved while working with time series: classification, prediction, anomaly detection, simulation and others and exactly deep learning can be leveraged to solve them on the state-of-the-art level. Some previous experience with time series/signal processing is useful for getting the most out of this session, but not required. Alex Honchar is developing production-ready AI solutions for small and medium businesses for the last 5 years, giving public speeches in Europe and blogging about ML and AI recent advances.

Data science is a very hands-on and practical field. Data science requires a solid foundation in mathematics and programming. As a data scientist, it is essential that you understand the theoretical and mathematical foundations of data science in order to be able to build reliable models with real-world applications. In data science and machine learning, mathematical skills are as important as programming skills. There are so many good packages that can be used for building predictive models.

Federated Learning enables visual models to be trained on-device, bringing advantages for user privacy (data need never leave the device), but challenges in terms of data diversity and quality. Whilst typical models in the datacenter are trained using data that are independent and identically distributed (IID), data at source are typically far from IID. Furthermore, differing quantities of data are typically available at each device (imbalance). In this work, we characterize the effect these real-world data distributions have on distributed learning, using as a benchmark the standard Federated Averaging (FedAvg) algorithm. To do so, we introduce two new large-scale datasets for species and landmark classification, with realistic per-user data splits that simulate real-world edge learning scenarios. We also develop two new algorithms (FedVC, FedIR) that intelligently resample and reweight over the client pool, bringing large improvements in accuracy and stability in training.