This work examines the convergence of stochastic gradient-based optimization algorithms that use early stopping based on a validation function. The form of early stopping we consider is that optimization terminates when the norm of the gradient of a validation function falls below a threshold. We derive conditions that guarantee this stopping rule is well-defined, and provide bounds on the expected number of iterations and gradient evaluations needed to meet this criterion. The guarantee accounts for the distance between the training and validation sets, measured with the Wasserstein distance. We develop the approach in the general setting of a first-order optimization algorithm, with possibly biased update directions subject to a geometric drift condition. We then derive bounds on the expected running time for early stopping variants of several algorithms, including stochastic gradient descent (SGD), decentralized SGD (DSGD), and the stochastic variance reduced gradient (SVRG) algorithm. Finally, we consider the generalization properties of the iterate returned by early stopping.

Invertible flow-based generative models are an effective method for learning to generate samples, while allowing for tractable likelihood computation and inference. However, the invertibility requirement restricts models to have the same latent dimensionality as the inputs. This imposes significant architectural, memory, and computational costs, making them more challenging to scale than other classes of generative models such as Variational Autoencoders (VAEs). We propose a generative model based on probability flows that does away with the bijectivity requirement on the model and only assumes injectivity. This also provides another perspective on regularized autoencoders (RAEs), with our final objectives resembling RAEs with specific regularizers that are derived by lower bounding the probability flow objective. We empirically demonstrate the promise of the proposed model, improving over VAEs and AEs in terms of sample quality.

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional H\'enon map at the classical parameters. The task is to determine whether a trajectory will exceed a threshold after a set number of time steps into the future. This task has a geometric interpretation within the dynamics of the H\'enon map, which we use to gauge the performance of the neural networks that are used in this work. We analyze the dependence of the success rate of the ML models on the prediction time $T$ , the number of training samples $N_T$ and the size of the network $N_p$. We observe that in order to maintain a certain accuracy, $N_T \propto exp(2 h T)$ and $N_p \propto exp(hT)$, where $h$ is the topological entropy. Similar relations between the intrinsic chaotic properties of the dynamics and ML parameters might be observable in other systems as well.

The multiplicative weights method is an algorithm for the problem of prediction with expert advice. It achieves the minimax regret asymptotically if the number of experts is large, and the time horizon is known in advance. Optimal algorithms are also known if there are exactly two or three experts, and the time horizon is known in advance. In the anytime setting, where the time horizon is not known in advance, algorithms can be obtained by the doubling trick, but they are not optimal, let alone practical. No minimax optimal algorithm was previously known in the anytime setting, regardless of the number of experts. We design the first minimax optimal algorithm for minimizing regret in the anytime setting. We consider the case of two experts, and prove that the optimal regret is $\gamma \sqrt{t} / 2$ at all time steps $t$, where $\gamma$ is a natural constant that arose 35 years ago in studying fundamental properties of Brownian motion. The algorithm is designed by considering a continuous analogue, which is solved using ideas from stochastic calculus.

Aspect based Sentiment Analysis is a major subarea of sentiment analysis. Many supervised and unsupervised approaches have been proposed in the past for detecting and analyzing the sentiment of aspect terms. In this paper, a graph-based semi-supervised learning approach for aspect term extraction is proposed. In this approach, every identified token in the review document is classified as aspect or non-aspect term from a small set of labeled tokens using label spreading algorithm. The k-Nearest Neighbor (kNN) for graph sparsification is employed in the proposed approach to make it more time and memory efficient. The proposed work is further extended to determine the polarity of the opinion words associated with the identified aspect terms in review sentence to generate visual aspect-based summary of review documents. The experimental study is conducted on benchmark and crawled datasets of restaurant and laptop domains with varying value of labeled instances. The results depict that the proposed approach could achieve good result in terms of Precision, Recall and Accuracy with limited availability of labeled data.

In this paper, we propose an approach for Facial Expressions Recognition (FER) based on a deep multi-facial patches aggregation network. Deep features are learned from facial patches using deep sub-networks and aggregated within one deep architecture for expression classification . Several problems may affect the performance of deep-learning based FER approaches, in particular, the small size of existing FER datasets which might not be sufficient to train large deep learning networks. Moreover, it is extremely time-consuming to collect and annotate a large number of facial images. To account for this, we propose two data augmentation techniques for facial expression generation to expand FER labeled training datasets. We evaluate the proposed framework on three FER datasets. Results show that the proposed approach achieves state-of-art FER deep learning approaches performance when the model is trained and tested on images from the same dataset. Moreover, the proposed data augmentation techniques improve the expression recognition rate, and thus can be a solution for training deep learning FER models using small datasets. The accuracy degrades significantly when testing for dataset bias.

In recent years, multi-access edge computing (MEC) is a key enabler for handling the massive expansion of Internet of Things (IoT) applications and services. However, energy consumption of a MEC network depends on volatile tasks that induces risk for energy demand estimations. As an energy supplier, a microgrid can facilitate seamless energy supply. However, the risk associated with energy supply is also increased due to unpredictable energy generation from renewable and non-renewable sources. Especially, the risk of energy shortfall is involved with uncertainties in both energy consumption and generation. In this paper, we study a risk-aware energy scheduling problem for a microgrid-powered MEC network. First, we formulate an optimization problem considering the conditional value-at-risk (CVaR) measurement for both energy consumption and generation, where the objective is to minimize the loss of energy shortfall of the MEC networks and we show this problem is an NP-hard problem. Second, we analyze our formulated problem using a multi-agent stochastic game that ensures the joint policy Nash equilibrium, and show the convergence of the proposed model. Third, we derive the solution by applying a multi-agent deep reinforcement learning (MADRL)-based asynchronous advantage actor-critic (A3C) algorithm with shared neural networks. This method mitigates the curse of dimensionality of the state space and chooses the best policy among the agents for the proposed problem. Finally, the experimental results establish a significant performance gain by considering CVaR for high accuracy energy scheduling of the proposed model than both the single and random agent models.

Head mounted displays bring eye tracking into daily use and this raises privacy concerns for users. Privacy-preservation techniques such as differential privacy mechanisms are recently applied to the eye tracking data obtained from such displays; however, standard differential privacy mechanisms are vulnerable to temporal correlations in the eye movement features. In this work, a transform coding based differential privacy mechanism is proposed for the first time in the eye tracking literature to further adapt it to statistics of eye movement feature data by comparing various low-complexity methods. Fourier Perturbation Algorithm, which is a differential privacy mechanism, is extended and a scaling mistake in its proof is corrected. Significant reductions in correlations in addition to query sensitivities are illustrated, which provide the best utility-privacy trade-off in the literature for the eye tracking dataset used. The differentially private eye movement data are evaluated also for classification accuracies for gender and document-type predictions to show that higher privacy is obtained without a reduction in the classification accuracies by using proposed methods.

More recently there has been an interest in density forecasts for the hourly prices, motivated by considerations of risk management. See [1,2] for extensive reviews. In this paper, we provide a new formulation with a focus upon price spreads, and specifically, we forecast the density functions for the intraday spreads in the day-ahead prices. The optimal operation of storage facilities, e.g., batteries and electric vehicles, or load shifting programmes, e.g., demand-side management, over daily cycles depends upon these spreads if they are operated as merchants, arbitraging buying and selling from the wholesale market. Furthermore, if the risk is a consideration, analysis of the mean differences in price levels would be inadequate, and we therefore directly estimate the density functions of all hourly spreads in prices at the day-ahead stage. These forecasts ahead of the day-ahead auctions would be needed to help traders decide whether they want to be buyers or sellers at each hour and thereby optimise their bids and offers. Our specification, estimation and forecasting of these arbitrage spreads are new and computationally-intensive. Based upon day-ahead forecasts for the drivers of electricity prices, such as demand, wind and solar production, gas and coal prices, forecasts for electricity price levels have been proposed from various methods, e.g., [3-6] and some for price densities [1,7], but apparently no methods have been developed specifically for forecasting intraday spread densities. Until recently storage assets, such as pumped hydro storage, would regularly store energy at night and discharge at the daily peak demand periods, which were quite predictable. However with the penetration of wind and especially solar generating facilities, the peak and trough hours in prices move around the day and in sunny locations with substantial solar energy, e.g., California, the lowest prices may often be in the middle of the day [8].

This paper addresses the problem of learning the optimal feedback policy for a nonlinear stochastic dynamical system with continuous state space, continuous action space and unknown dynamics. Feedback policies are complex objects that typically need a large dimensional parametrization, which makes Reinforcement Learning algorithms that search for an optimum in this large parameter space, sample inefficient and subject to high variance. We propose a "decoupling" principle that drastically reduces the feedback parameter space while still remaining near-optimal to the fourth-order in a small noise parameter. Based on this principle, we propose a decoupled data-based control (D2C) algorithm that addresses the stochastic control problem: first, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, a linear closed-loop control is developed around this nominal trajectory using only a simulation model. Empirical evidence suggests significant reduction in training time, as well as the training variance, compared to other state of the art Reinforcement Learning algorithms.