Quantifying bias from dependent left truncation in survival analyses of real world data

In real world data (RWD) studies, observed datasets are often subject to left truncation, which can bias estimates of survival parameters. Standard methods can only suitably account for left truncation when survival and entry time are independent. Therefore, in the dependent left truncation setting, it is important to quantify the magnitude and direction of estimator bias to determine whether an analysis provides valid results. We conduct simulation studies of common RWD analytic settings in order to determine when standard analysis provides reliable estimates, and to identify factors that contribute most to estimator bias. We also outline a procedure for conducting a simulation-based sensitivity analysis for an arbitrary dataset subject to dependent left truncation. Our simulation results show that when comparing a truncated real-world arm to a non-truncated arm, we observe the estimated hazard ratio biased upwards, providing conservative inference. The most important data-generating parameter contributing to bias is the proportion of left truncated patients, given any level of dependence between survival and entry time. For specific datasets and analyses that may differ from our example, we recommend applying our sensitivity analysis approach to determine how results would change given varying proportions of truncation.

American Option Pricing with Importance Sampling and Shifted Regressions

This paper proposes a new method for pricing American options that uses importance sampling to reduce estimator bias and variance in simulation-and-regression based methods. Our suggested method uses regressions under the importance measure directly, instead of under the nominal measure as is the standard, to determine the optimal early exercise strategy. Our numerical results show that this method successfully reduces the bias plaguing the standard importance sampling method across a wide range of moneyness and maturities, with negligible change to estimator variance. When a low number of paths is used, our method always improves on the standard method and reduces average root mean squared error of estimated option prices by 22.5%.

A survey on deep learning-based Monte Carlo denoising

Monte Carlo (MC) integration is used ubiquitously in realistic image synthesis because of its flexibility and generality. However, the integration has to balance estimator bias and variance, which causes visually distracting noise with low sample counts. Existing solutions fall into two categories, in-process sampling schemes and post-processing reconstruction schemes. This report summarizes recent trends in the post-processing reconstruction scheme. Recent years have seen increasing attention and significant progress in denoising MC rendering with deep learning, by training neural networks to reconstruct denoised rendering results from sparse MC samples. Many of these techniques show promising results in real-world applications, and this report aims to provide an assessment of these approaches for practitioners and researchers.

Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing Its Gradient Estimator Bias

Equilibrium Propagation is a biologically-inspired algorithm that trains convergent recurrent neural networks with a local learning rule. This approach constitutes a major lead to allow learning-capable neuromophic systems and comes with strong theoretical guarantees. Equilibrium propagation operates in two phases, during which the network is let to evolve freely and then “nudged” toward a target; the weights of the network are then updated based solely on the states of the neurons that they connect. The weight updates of Equilibrium Propagation have been shown mathematically to approach those provided by Backpropagation Through Time (BPTT), the mainstream approach to train recurrent neural networks, when nudging is performed with infinitely small strength. In practice, however, the standard implementation of Equilibrium Propagation does not scale to visual tasks harder than MNIST. In this work, we show that a bias in the gradient estimate of equilibrium propagation, inherent in the use of finite nudging, is responsible for this phenomenon and that canceling it allows training deep convolutional neural networks. We show that this bias can be greatly reduced by using symmetric nudging (a positive nudging and a negative one). We also generalize Equilibrium Propagation to the case of cross-entropy loss (by opposition to squared error). As a result of these advances, we are able to achieve a test error of 11.7% on CIFAR-10, which approaches the one achieved by BPTT and provides a major improvement with respect to the standard Equilibrium Propagation that gives 86% test error. We also apply these techniques to train an architecture with unidirectional forward and backward connections, yielding a 13.2% test error. These results highlight equilibrium propagation as a compelling biologically-plausible approach to compute error gradients in deep neuromorphic systems.

Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options

We present the Forest of Stochastic Trees (FOST) method for pricing multiple exercise options by simulation. The proposed method uses stochastic trees in place of binomial trees in the Forest of Trees algorithm originally proposed to value swing options, hence extending that method to allow for a multi-dimensional underlying process. The FOST can also be viewed as extending the stochastic tree method for valuing (single exercise) American-style options to multiple exercise options. The proposed valuation method results in positively- and negatively-biased estimators for the true option value. We prove the sign of the estimator bias and show that these estimators are consistent for the true option value. This method is of particular use in cases where there is potentially a large number of assets underlying the contract and/or the underlying price process depends on multiple risk factors. Numerical results are presented to illustrate the method.

Redukcja efektu brzegowego w estymacji jądrowej wybranych charakterystyk funkcyjnych zmiennej losowej

For a random variable with bounded support, the kernel estimation of functional characteristics may lead to the occurrence of the so-called boundary effect. In the case of the kernel density estimation it can mean an increase of the estimator bias in the areas near the ends of the support, and can lead to a situation where the estimator is not a density function in the support of a random variable. In the paper the procedures for reducing boundary effect for kernel estimators of density function, distribution function and regression function are analyzed. Modifications of the classical kernel estimators and examples of applications of these procedures in the analysis of the functional characteristics relating to gross national product per capita are presented. The advantages of procedures are indicated taking into account the reduction of the bias in the boundary region of the support of the random variable considered.