A traditional approach to initialization in deep neural networks (DNNs) is to sample the network weights randomly for preserving the variance of pre-activations. On the other hand, several studies show that during the training process, the distribution of stochastic gradients can be heavy-tailed especially for small batch sizes. In this case, weights and therefore pre-activations can be modeled with a heavy-tailed distribution that has an infinite variance but has a finite (non-integer) fractional moment of order $s$ with $s<2$. Motivated by this fact, we develop initialization schemes for fully connected feed-forward networks that can provably preserve any given moment of order $s \in (0, 2]$ over the layers for a class of activations including ReLU, Leaky ReLU, Randomized Leaky ReLU, and linear activations. These generalized schemes recover traditional initialization schemes in the limit $s \to 2$ and serve as part of a principled theory for initialization. For all these schemes, we show that the network output admits a finite almost sure limit as the number of layers grows, and the limit is heavy-tailed in some settings. This sheds further light into the origins of heavy tail during signal propagation in DNNs. We prove that the logarithm of the norm of the network outputs, if properly scaled, will converge to a Gaussian distribution with an explicit mean and variance we can compute depending on the activation used, the value of s chosen and the network width. We also prove that our initialization scheme avoids small network output values more frequently compared to traditional approaches. Furthermore, the proposed initialization strategy does not have an extra cost during the training procedure. We show through numerical experiments that our initialization can improve the training and test performance.

Randomized smoothing has achieved state-of-the-art certified robustness against $l_2$-norm adversarial attacks. However, it is not wholly resolved on how to find the optimal base classifier for randomized smoothing. In this work, we employ a Smoothed WEighted ENsembling (SWEEN) scheme to improve the performance of randomized smoothed classifiers. We theoretically analyze the expressive power of the SWEEN function class and show that SWEEN can be trained to achieve near-optimal risk in the randomized smoothing regime. We also develop an adaptive prediction algorithm to reduce the prediction and certification cost of SWEEN models. Extensive experiments show that SWEEN models outperform the upper envelope of their corresponding candidate models by a large margin. Moreover, SWEEN models constructed using a few small models can achieve comparable performance to a single large model with a notable reduction in training time.

Time series forecasting is ubiquitous in real-world applications. Examples include forecasting of demand to fill up inventories, economic growth forecasts to inform policies, and predicting stock prices to guide financial decisions. Forecasting is also a fruitful area for machine learning research, and pure and hybrid machine learning approaches have recently achieved state-of-the-art performance [1, 2]. In practice, forecasting involves a number of steps: we first need to specify, fit and select an appropriate model, and then evaluate and deploy it. There are various open-source toolboxes that help us implement these steps. However, most existing toolboxes are limited in important respects.

Several real-world applications are characterized by data that exhibit a complex structure that can be represented using graphs. The popularity of deep learning techniques renewed the interest in neural architectures able to process these patterns, inspired by the Graph Neural Network (GNN) model. GNNs encode the state of the nodes of the graph by means of an iterative diffusion procedure that, during the learning stage, must be computed at every epoch, until the fixed point of a learnable state transition function is reached, propagating the information among the neighbouring nodes. We propose a novel approach to learning in GNNs, based on constrained optimization in the Lagrangian framework. Learning both the transition function and the node states is the outcome of a joint process, in which the state convergence procedure is implicitly expressed by a constraint satisfaction mechanism, avoiding iterative epoch-wise procedures and the network unfolding. Our computational structure searches for saddle points of the Lagrangian in the adjoint space composed of weights, nodes state variables and Lagrange multipliers. This process is further enhanced by multiple layers of constraints that accelerate the diffusion process. An experimental analysis shows that the proposed approach compares favourably with popular models on several benchmarks.

We estimate the Lipschitz constants of the gradient of a deep neural network and the network itself with respect to the full set of parameters. We first develop estimates for a deep feed-forward densely connected network and then, in a more general framework, for all neural networks that can be represented as solutions of controlled ordinary differential equations, where time appears as continuous depth. These estimates can be used to set the step size of stochastic gradient descent methods, which is illustrated for one example method.

The upper confidence reinforcement learning (UCRL2) strategy introduced in (Jaksch et al., 2010) is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite its nice and generic theoretical regret guarantees, this strategy and its variants have remained until now mostly theoretical as numerical experiments on simple environments exhibit long burn-in phases before the learning takes place. Motivated by practical efficiency, we present UCRL3, following the lines of UCRL2, but with two key modifications: First, it uses state-of-the-art time-uniform concentration inequalities, to compute confidence sets on the reward and transition distributions for each state-action pair. To further tighten exploration, we introduce an adaptive computation of the support of each transition distributions. This enables to revisit the extended value iteration procedure to optimize over distributions with reduced support by disregarding low probability transitions, while still ensuring near-optimism. We demonstrate, through numerical experiments on standard environments, that reducing exploration this way yields a substantial numerical improvement compared to UCRL2 and its variants. On the theoretical side, these key modifications enable to derive a regret bound for UCRL3 improving on UCRL2, that for the first time makes appear a notion of local diameter and effective support, thanks to variance-aware concentration bounds.

Companies have considered adoption of various high-level artificial intelligence (AI) principles for responsible AI, but there is less clarity on how to implement these principles as organizational practices. This paper reviews the principles-to-practices gap. We outline five explanations for this gap ranging from a disciplinary divide to an overabundance of tools. In turn, we argue that an impact assessment framework which is broad, operationalizable, flexible, iterative, guided, and participatory is a promising approach to close the principles-to-practices gap. Finally, to help practitioners with applying these recommendations, we review a case study of AI's use in forest ecosystem restoration, demonstrating how an impact assessment framework can translate into effective and responsible AI practices.

In recent years, we have seen an unprecedented explosion of interest in applying artificial intelligence and machine learning to a variety of quantitative finance problems, ranging from derivatives pricing and risk management to market forecasting and algo trading. In fact, Artificial Intelligence and Machine Learning are now seen as the greatest enablers of competitive advantage in the finance sector. Both applications use state-of-the-art Machine Learning techniques – LSTM neural net and NEAT genetic algorithm – in combination with news sentiment.

Mike Tyson famously said that "Everyone has a plan until they get punched in the mouth". Every company had a strategic plan coming into 2020. Then, Covid-19 walked into the ring. Insurance has been hit hard by Covid-19 and economic hardship. With many insurers focused on cash conservation, leading insurers can emerge from the crisis even stronger if they make smart investments in AI. Insurers' massive customer datasets and their famously manual processes create some'quick win' AI opportunities.

"Helsinki aims to be the most functional city in the world. Innovation to support the best urban life conditions possible is in the core of our strategy. As such, the promotion of sustainable modes of transport is considered as a high priority. We aim for a pleasant environment, good accessibility, and fluent transport as well as the reduction of the environmental impact. In my opinion, the FABULOS project can greatly contribute to achieving this goal by demonstrating the benefits of autonomous public transportation," the Mayor of Helsinki, Jan Vapaavuori, said in a statement.