Multistage Portfolio Optimization: A Duality Result in Conic Market Models

We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability space and finite-horizon discrete time steps. This framework allows us to compare vector-valued portfolios under a partial ordering, so that our model does not require liquidation into some numeraire at terminal time. We embed the vector-valued portfolio problem into the set-optimization framework, and generate a problem dual to portfolio optimization. Using recent results in the development of set optimization, we then show that a strong duality relationship holds between the problems

Log-Concave Duality in Estimation and Control

In this paper we generalize the estimation-control duality that exists in the linear-quadratic-Gaussian setting. We extend this duality to maximum a posteriori estimation of the system's state, where the measurement and dynamical system noise are independent log-concave random variables. More generally, we show that a problem which induces a convex penalty on noise terms will have a dual control problem. We provide conditions for strong duality to hold, and then prove relaxed conditions for the piecewise linear-quadratic case. The results have applications in estimation problems with nonsmooth densities, such as log-concave maximum likelihood densities. We conclude with an example reconstructing optimal estimates from solutions to the dual control problem, which has implications for sharing solution methods between the two types of problems

Finger Pain out of Proportion to Exam: A Case of Occult Hydrofluoric Acid Toxicity

Background: Hydrofluoric acid (HFA) toxicity can have significant morbidity and even mortality associated with seemingly small exposures. As a result of a delayed time to symptom onset, low concentration exposures may present as a diagnostic dilemma. Objective: To demonstrate an atypical case presentation of HFA exposure, the inherent diagnostic difficulty, and subtle clues to confirming the diagnosis. Case Report: We present the case of a 21 year old male day laborer who presented to the emergency department 12 hours after exposure to a cleaning agent used to “polish” metal with significant finger pain, minimal physical exam findings, and refractory to analgesics. He demonstrated hypocalcemia and hypomagnesemia. The patient reported symptom resolution after treatment with topical calcium gluconate. Conclusion: This case demonstrates the importance of considering HFA toxicity in any patient who presents with pain, minimal physical exam findings, after exposure to an unknown chemical cleaning agent.Screening for the common electrolyte depletion associated with HFA toxicity may help to confirm the diagnosis as well as guide therapy

Fused Density Estimation: Theory and Methods

In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide theoretical support for fused density estimation by proving that the squared Hellinger rate of convergence for the estimator achieves the minimax bound over univariate densities of log-bounded variation. We reduce the original variational formulation in order to transform it into a tractable, finite-dimensional quadratic program. Because random variables on geometric networks are simple generalizations of the univariate case, this method also provides a useful tool for univariate density estimation. Lastly, we apply this method and assess its performance on examples in the univariate and geometric network setting. We compare the performance of different optimization techniques to solve the problem, and use these results to inform recommendations for the computation of fused density estimators

DeepFake Detection with Inconsistent Head Poses: Reproducibility and Analysis

Applications of deep learning to synthetic media generation allow the creation of convincing forgeries, called DeepFakes, with limited technical expertise. DeepFake detection is an increasingly active research area. In this paper, we analyze an existing DeepFake detection technique based on head pose estimation, which can be applied when fake images are generated with an autoencoder-based face swap. Existing literature suggests that this method is an effective DeepFake detector, and its motivating principles are attractively simple. With an eye towards using these principles to develop new DeepFake detectors, we conduct a reproducibility study of the existing method. We conclude that its merits are dramatically overstated, despite its celebrated status. By investigating this discrepancy we uncover a number of important and generalizable insights related to facial landmark detection, identity-agnostic head pose estimation, and algorithmic bias in DeepFake detectors. Our results correct the current literature's perception of state of the art performance for DeepFake detection