Exploiting the Statistics of Learning and Inference

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by exploiting their inherent statistical nature. We propose algorithms that exploit the redundancy of data relative to a model by subsampling data-cases for every update and reasoning about the uncertainty created in this process. In the context of learning we propose to test for the probability that a stochastically estimated gradient points more than 180 degrees in the wrong direction. In the context of MCMC sampling we use stochastic gradients to improve the efficiency of MCMC updates, and hypothesis tests based on adaptive mini-batches to decide whether to accept or reject a proposed parameter update. Finally, we argue that in the context of likelihood free MCMC one needs to store all the information revealed by all simulations, for instance in a Gaussian process. We conclude that Bayesian methods will remain to play a crucial role in the era of big data and big simulations, but only if we overcome a number of computational challenges.Comment: Proceedings of the NIPS workshop on "Probabilistic Models for Big Data

In Defense of the Dealers: Why the SEC Should Allow Substituted Compliance with the European Union for Security-Based Swap Dealers

Following the 2008–2009 financial crisis, legislators around the world enacted laws that regulated the over-the-counter (OTC) derivatives markets for the first time. These laws, though necessary, have duplicative requirements that dampen market efficiency. In the United States, the Securities and Exchange Commission is contemplating a “substituted compliance” regime with other jurisdictions. This regime would allow market participants to comply with one jurisdiction’s requirements for certain transactions, rather than the requirements of multiple jurisdictions. This Note argues that the SEC should allow substituted compliance for OTC derivatives, but only for dealers located in the United States and European Union. Some advocate for a broader substituted compliance regime. These arguments, however, overlook nuances of the SEC’s announced approach. Others argue that the SEC should avoid substituted compliance altogether. Ultimately, if the SEC allows substituted compliance narrowly and thoughtfully, it could preserve the economic benefits of a domestic financial market, while preventing some causes of the recent financial crisis

One Particle Hilbertspace of 2+1 dimensional Gravity using Non commuting Coordinates

After a review of multi particle solutions in classical 2+1 dimensional gravity we will construct a one particle Hilbert space. As we will use a curved momentum space, the coordinates $x^\mu$ are represented as non commuting Hermitian operators on this Hilbertspace. Finally we will indicate how to construct a Schrodinger equation.Comment: 4 pages Latex, 2 eps figures, uses espcr.sty; Talk given at the Second Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, 17-21 september 199

In Defense of the Dealers: Why the SEC Should Allow Substituted Compliance with the European Union for Security-Based Swap Dealers

Following the 2008–2009 financial crisis, legislators around the world enacted laws that regulated the over-the-counter (OTC) derivatives markets for the first time. These laws, though necessary, have duplicative requirements that dampen market efficiency. In the United States, the Securities and Exchange Commission is contemplating a “substituted compliance” regime with other jurisdictions. This regime would allow market participants to comply with one jurisdiction’s requirements for certain transactions, rather than the requirements of multiple jurisdictions. This Note argues that the SEC should allow substituted compliance for OTC derivatives, but only for dealers located in the United States and European Union. Some advocate for a broader substituted compliance regime. These arguments, however, overlook nuances of the SEC’s announced approach. Others argue that the SEC should avoid substituted compliance altogether. Ultimately, if the SEC allows substituted compliance narrowly and thoughtfully, it could preserve the economic benefits of a domestic financial market, while preventing some causes of the recent financial crisis