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This work considers reversed evolution in dynamical systems. In particular, asymptotic behavior of chaotic systems, when their orbits evolve backwards in time. Reversed dynamics reveals important aspects of the trajectories, such as a new…

The drawdown process of an one-dimensional regular diffusion process $X$ is given by $X$ reflected at its running maximum. The drawup process is given by $X$ reflected at its running minimum. We calculate the probability that a drawdown…

In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a…

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…

We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called {\it probability of drawdown}, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its…

Cycles in graphs often signify interesting processes. For example, cyclic trading patterns can indicate inefficiencies or economic dependencies in trade networks, cycles in food webs can identify fragile dependencies in ecosystems, and…

Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled…

We consider the multi-period portfolio optimization problem with a single asset that can be held long or short. Due to the presence of transaction costs, maximizing the immediate reward at each period may prove detrimental, as frequent…

Financial markets across all asset classes are known to exhibit trends. These trends have been exploited by traders for decades. Here, we empirically measure when trends revert, based on 30 years of daily futures prices for equity indices,…

It is suggested to consider long term trends of financial markets as a growth phenomenon. The question that is asked is what conditions are needed for a long term sustainable growth or contraction in a financial market? The paper discuss…

In this work we show that prediction uncertainty estimates gleaned from deep learning models can be useful inputs for influencing the relative allocation of risk capital across trades. In this way, consideration of uncertainty is important…

A significant challenge in maintaining real-world machine learning models is responding to the continuous and unpredictable evolution of data. Most practitioners are faced with the difficult question: when should I retrain or update my…

In multi-echelon inventory systems the performance of a given node is affected by events that occur at many other nodes and in many other time periods. For example, a supply disruption upstream will have an effect on downstream,…

Although sparse neural networks have been studied extensively, the focus has been primarily on accuracy. In this work, we focus instead on network structure, and analyze three popular algorithms. We first measure performance when structure…

Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network…

Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian. Prior work has identified critical initialization schemes…

Game theory has traditionally had a relatively limited view of risk based on how a player's expected reward is impacted by the uncertainty of the actions of other players. Recently, a new game-theoretic approach provides a more holistic…

A decision maker records measurements of a finite-state Markov chain corrupted by noise. The goal is to decide when the Markov chain hits a specific target state. The decision maker can choose from a finite set of sampling intervals to pick…

In the era of exceptionally data-hungry models, careful selection of the training data is essential to mitigate the extensive costs of deep learning. Data pruning offers a solution by removing redundant or uninformative samples from the…

Customer retention is one of the primary goals in the area of customer relationship management. A mass of work exists in which machine learning models or business rules are established to predict churn. However, targeting users at an early…