arXiv subjects

Alain Kornhauser

Publications and source records attributed to Alain Kornhauser.

4 recordsLinked to original sources

arXiv2023

On the properties of Gaussian Copula Mixture Models

This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of its likelihood function. Additionally, the paper proposes extended Expectation Maximum algorithms to estimate parameters for the mixture of copulas. The marginal distributions corresponding to each component are estimated separately using nonparametric statistical methods. In the experiment, GCMM demonstrates improved goodness-of-fitting compared to GMM when using the same number of clusters. Furthermore, GCMM has the ability to leverage un-synchronized data across dimensions for more comprehensive data analysis.

cs.LG↗

arXiv2023

Market Making and Pricing of Financial Derivatives based on Road Travel Times

Travel time derivatives are financial instruments that derive their value from road travel times, serving as an underlying asset that cannot be directly traded. Within the transportation domain, these derivatives are proposed as a more comprehensive approach to value pricing. They enable road pricing based not only on the level of travel time but also its volatility. In the financial market, travel time derivatives are introduced as innovative hedging instruments to mitigate market risk, particularly in light of recent stress experienced by the crypto market and traditional banking sector. The paper focuses on three main aspects: (1) the motivation behind the introduction of these derivatives, driven by the demand for hedging; (2) exploring the potential market for these instruments; and (3) delving into the product design and pricing schemes associated with them. The pricing schemes are devised by utilizing real-time travel time data captured by sensors. These data are modeled using Ornstein-Uhlenbeck processes and, more broadly, continuous time autoregressive moving average (CARMA) models. The calibration of these models is achieved through a hidden factor model, which describes the dynamics of travel time processes. The risk-neutral pricing principle is then employed to determine the prices of the derivatives, employing well-designed procedures to identify the market value of risk.

stat.AP↗

arXiv2017

Beyond Grand Theft Auto V for Training, Testing and Enhancing Deep Learning in Self Driving Cars

As an initial assessment, over 480,000 labeled virtual images of normal highway driving were readily generated in Grand Theft Auto V's virtual environment. Using these images, a CNN was trained to detect following distance to cars/objects ahead, lane markings, and driving angle (angular heading relative to lane centerline): all variables necessary for basic autonomous driving. Encouraging results were obtained when tested on over 50,000 labeled virtual images from substantially different GTA-V driving environments. This initial assessment begins to define both the range and scope of the labeled images needed for training as well as the range and scope of labeled images needed for testing the definition of boundaries and limitations of trained networks. It is the efficacy and flexibility of a "GTA-V"-like virtual environment that is expected to provide an efficient well-defined foundation for the training and testing of Convolutional Neural Networks for safe driving. Additionally, described is the Princeton Virtual Environment (PVE) for the training, testing and enhancement of safe driving AI, which is being developed using the video-game engine Unity. PVE is being developed to recreate rare but critical corner cases that can be used in re-training and enhancing machine learning models and understanding the limitations of current self driving models. The Florida Tesla crash is being used as an initial reference.

cs.CV↗

arXiv2015

DeepDriving: Learning Affordance for Direct Perception in Autonomous Driving

Today, there are two major paradigms for vision-based autonomous driving systems: mediated perception approaches that parse an entire scene to make a driving decision, and behavior reflex approaches that directly map an input image to a driving action by a regressor. In this paper, we propose a third paradigm: a direct perception approach to estimate the affordance for driving. We propose to map an input image to a small number of key perception indicators that directly relate to the affordance of a road/traffic state for driving. Our representation provides a set of compact yet complete descriptions of the scene to enable a simple controller to drive autonomously. Falling in between the two extremes of mediated perception and behavior reflex, we argue that our direct perception representation provides the right level of abstraction. To demonstrate this, we train a deep Convolutional Neural Network using recording from 12 hours of human driving in a video game and show that our model can work well to drive a car in a very diverse set of virtual environments. We also train a model for car distance estimation on the KITTI dataset. Results show that our direct perception approach can generalize well to real driving images. Source code and data are available on our project website.

cs.CV↗