42,316 research outputs found
Quick Search for Rare Events
Rare events can potentially occur in many applications. When manifested as
opportunities to be exploited, risks to be ameliorated, or certain features to
be extracted, such events become of paramount significance. Due to their
sporadic nature, the information-bearing signals associated with rare events
often lie in a large set of irrelevant signals and are not easily accessible.
This paper provides a statistical framework for detecting such events so that
an optimal balance between detection reliability and agility, as two opposing
performance measures, is established. The core component of this framework is a
sampling procedure that adaptively and quickly focuses the
information-gathering resources on the segments of the dataset that bear the
information pertinent to the rare events. Particular focus is placed on
Gaussian signals with the aim of detecting signals with rare mean and variance
values
Adaptive Importance Sampling for Performance Evaluation and Parameter Optimization of Communication Systems
We present new adaptive importance sampling techniques based on stochastic Newton recursions. Their applicability to the performance evaluation of communication systems is studied. Besides bit-error rate (BER) estimation, the techniques are used for system parameter optimization. Two system models that are analytically tractable are employed to demonstrate the validity of the techniques. As an application to situations that are analytically intractable and numerically intensive, the influence of crosstalk in a wavelength-division multiplexing (WDM) crossconnect is assessed. In order to consider a realistic system model, optimal setting of thresholds in the detector is carried out while estimating error rate performances. Resulting BER estimates indicate that the tolerable crosstalk levels are significantly higher than predicted in the literature. This finding has a strong impact on the design of WDM networks. Power penalties induced by the addition of channels can also be accurately predicted in short run-time
Operational risk management and new computational needs in banks
Basel II banking regulation introduces new needs for computational schemes. They involve both optimal stochastic control, and large scale simulations of decision processes of preventing low-frequency high loss-impact events. This paper will first state the problem and present its parameters. It then spells out the equations that represent a rational risk management behavior and link together the variables: Levy processes are used to model operational risk losses, where calibration by historical loss databases is possible ; where it is not the case, qualitative variables such as quality of business environment and internal controls can provide both costs-side and profits-side impacts. Among other control variables are business growth rate, and efficiency of risk mitigation. The economic value of a policy is maximized by resolving the resulting Hamilton-Jacobi-Bellman type equation. Computational complexity arises from embedded interactions between 3 levels: * Programming global optimal dynamic expenditures budget in Basel II context, * Arbitraging between the cost of risk-reduction policies (as measured by organizational qualitative scorecards and insurance buying) and the impact of incurred losses themselves. This implies modeling the efficiency of the process through which forward-looking measures of threats minimization, can actually reduce stochastic losses, * And optimal allocation according to profitability across subsidiaries and business lines. The paper next reviews the different types of approaches that can be envisaged in deriving a sound budgetary policy solution for operational risk management, based on this HJB equation. It is argued that while this complex, high dimensional problem can be resolved by taking some usual simplifications (Galerkin approach, imposing Merton form solutions, viscosity approach, ad hoc utility functions that provide closed form solutions, etc.) , the main interest of this model lies in exploring the scenarios in an adaptive learning framework ( MDP, partially observed MDP, Q-learning, neuro-dynamic programming, greedy algorithm, etc.). This makes more sense from a management point of view, and solutions are more easily communicated to, and accepted by, the operational level staff in banks through the explicit scenarios that can be derived. This kind of approach combines different computational techniques such as POMDP, stochastic control theory and learning algorithms under uncertainty and incomplete information. The paper concludes by presenting the benefits of such a consistent computational approach to managing budgets, as opposed to a policy of operational risk management made up from disconnected expenditures. Such consistency satisfies the qualifying criteria for banks to apply for the AMA (Advanced Measurement Approach) that will allow large economies of regulatory capital charge under Basel II Accord.REGULAR - Operational risk management, HJB equation, Levy processes, budget optimization, capital allocation
Exploration of Reaction Pathways and Chemical Transformation Networks
For the investigation of chemical reaction networks, the identification of
all relevant intermediates and elementary reactions is mandatory. Many
algorithmic approaches exist that perform explorations efficiently and
automatedly. These approaches differ in their application range, the level of
completeness of the exploration, as well as the amount of heuristics and human
intervention required. Here, we describe and compare the different approaches
based on these criteria. Future directions leveraging the strengths of chemical
heuristics, human interaction, and physical rigor are discussed.Comment: 48 pages, 4 figure
Study of application of adaptive systems to the exploration of the solar system. Volume 1: Summary
The field of artificial intelligence to identify practical applications to unmanned spacecraft used to explore the solar system in the decade of the 80s is examined. If an unmanned spacecraft can be made to adjust or adapt to the environment, to make decisions about what it measures and how it uses and reports the data, it can become a much more powerful tool for the science community in unlocking the secrets of the solar system. Within this definition of an adaptive spacecraft or system, there is a broad range of variability. In terms of sophistication, an adaptive system can be extremely simple or as complex as a chess-playing machine that learns from its mistakes
Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces
The paper presents a new efficient and robust method for rare event
probability estimation for computational models of an engineering product or a
process returning categorical information only, for example, either success or
failure. For such models, most of the methods designed for the estimation of
failure probability, which use the numerical value of the outcome to compute
gradients or to estimate the proximity to the failure surface, cannot be
applied. Even if the performance function provides more than just binary
output, the state of the system may be a non-smooth or even a discontinuous
function defined in the domain of continuous input variables. In these cases,
the classical gradient-based methods usually fail. We propose a simple yet
efficient algorithm, which performs a sequential adaptive selection of points
from the input domain of random variables to extend and refine a simple
distance-based surrogate model. Two different tasks can be accomplished at any
stage of sequential sampling: (i) estimation of the failure probability, and
(ii) selection of the best possible candidate for the subsequent model
evaluation if further improvement is necessary. The proposed criterion for
selecting the next point for model evaluation maximizes the expected
probability classified by using the candidate. Therefore, the perfect balance
between global exploration and local exploitation is maintained automatically.
The method can estimate the probabilities of multiple failure types. Moreover,
when the numerical value of model evaluation can be used to build a smooth
surrogate, the algorithm can accommodate this information to increase the
accuracy of the estimated probabilities. Lastly, we define a new simple yet
general geometrical measure of the global sensitivity of the rare-event
probability to individual variables, which is obtained as a by-product of the
proposed algorithm.Comment: Manuscript CMAME-D-22-00532R1 (Computer Methods in Applied Mechanics
and Engineering
Fast Estimation of Outage Probabilities in MIMO Channels
Fast estimation methods for small outage probabilities of signaling in fading multiple-input multiple-output (MIMO) channels are developed. Communication over such channels is of much current interest, and quick and accurate methods for estimating outage capacities are needed. The methods described herein use adaptive importance sampling (IS) techniques as developed in a series of recent publications. Fast algorithms are provided for evaluating "nonergodic" capacities of Rayleigh fading MIMO channels. The methodology can be extended to more general models. Numerical results on outage capacity are provided, and these extend and complement known results in the literature
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