Presence Of Partial Information Research Articles

Overreaction and the value of information in a pandemic

This paper studies optimal mitigation and testing during a pandemic in the presence of partial information. We develop a stylized dynamic epidemiological model where the true number of infected individuals can only be partially inferred from two noisy signals: hospitalization and positivity rate. An egalitarian planner chooses the level of mitigation and testing, which respectively affect the infection rate and signal noise, at a certain economic cost. We first show that the planner is willing to pay a significant “information premium” to eliminate the uncertainty by extensive testing. However, if testing is prohibitively costly, then a stringent mitigation becomes optimal, as it partially substitutes for testing as an information acquisition device. Such policies were often criticized as excessive at the onset of the COVID-19 pandemic. We argue that this “optimal overreaction” is a result of the extreme costs of policy mistakes – such as high future casualties – and not due to an aversion to risk.

Robust pricing for airlines with partial information.

In the spot market for air cargo, airlines typically adopt dynamic pricing to tackle demand uncertainty, for which it is difficult to accurately estimate the distribution. This study addresses the problem where a dominant airline dynamically sets prices to sell its capacities within a two-phase sales period with only partial information. That partial information may show as the moments (upper and lower bounds and mean) and the median of the demand distribution. We model the problem of dynamic pricing as a distributional robust stochastic programming, which minimizes the expected regret value under the worst-case distribution in the presence of partial information. We further reformulate the proposed non-convex model to show that the closed-form formulae of the second-stage maximal expected regret are well-structured. We also design an efficient algorithm to characterize robust pricing strategies in a polynomial-sized running time. Using numerical analysis, we present several useful managerial insights for airline managers to strategically collect demand information and make prices for their capacities in different market situations. Moreover, we verify that additional information will not compromise the viability of the pricing strategies being implemented. Therefore, the method we present in this paper is easier for airlines to use.

A Combinatorial Solution to Causal Compatibility

Abstract Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for assessing causal compatibility is in the presence of partial information; i.e. when some of the variables are hidden/latent. This paper introduces the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called a possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency.

Localized Epidemic Detection in Networks with Overwhelming Noise

We consider the problem of detecting an epidemic in a population where individual diagnoses are extremely noisy. We show that exclusively local, approximate knowledge of the contact network suffices to accurately detect the epidemic. The motivation for this problem is the plethora of examples (influenza strains in humans, or computer viruses in smartphones, etc.) where reliable diagnoses are scarce, but noisy data plentiful. In flu or phone-viruses, exceedingly few infected people/phones are professionally diagnosed (only a small fraction go to a doctor) but less reliable secondary signatures (e.g., people staying home, or greater-than-typical upload activity) are more readily available. Our algorithm requires only local-neighbor knowledge of this graph, and in a broad array of settings that we describe, succeeds even when false negatives and false positives make up an overwhelming majority of the data available. Our results show it succeeds in the presence of partial information about the contact network, and also when are many (hundreds, in our examples) of initial patients-zero.

Stable solutions for multiple scenario cost allocation games with partial information

Multiple scenario cooperative games model situations where the worth of the coalitions is simultaneously valued in several scenarios or under different states of nature. For multiple scenario cost allocation games, we focus on the identification of those allocations which are stable in the sense that agents have no incentives to abandon the group. The stability of an allocation depends on how the quantities assigned to the coalitions are compared with the vector-valued worth of the coalition. Therefore, different extensions of the notion of core emerge, depending on how these comparisons are made. In this paper different notions of core for multiple scenario cost allocation games are studied, and the relationships between them and the existing core solutions are analyzed. We also address the inclusion in the model of partial information about the relative importance of the scenarios which often refers to the probabilities of occurrence. In order to identify allocations which are also stable in the presence of partial information, we extend the notions of core to this new setting, and provide results which permit the calculation of the corresponding sets of allocations. The potential applicability of our analysis is illustrated with the allocation of the total cost of the waste collection service between the different urban areas in the city of Seville.

A matrix factorization approach to graph compression with partial information

We address the problem of encoding a graph of order $$\mathsf {n}$$ into a graph of order $$\mathsf {k}<\mathsf {n}$$ in a way to minimize reconstruction error. This encoding is characterized in terms of a particular factorization of the adjacency matrix of the original graph. The factorization is determined as the solution of a discrete optimization problem, which is for convenience relaxed into a continuous, but equivalent, one. Our formulation does not require to have the full graph, but it can factorize the graph also in the presence of partial information. We propose a multiplicative update rule for the optimization task resembling the ones introduced for nonnegative matrix factorization, and convergence properties are proven. Experiments are conducted to assess the effectiveness of the proposed approach.

Conditional inference given partial information in contingency tables using Markov bases

AbstractIn this article, we review a Markov chain Monte Carlo (MCMC) algorithm for performing conditional inference in contingency tables in the presence of partial information using Markov bases, a key tool arising from the area known as algebraic statistics. We review applications of this algorithm to the problems of conditional exact tests, ecological inference, and disclosure limitation and illustrate how these problems fall naturally in the setting of inference with partial information. We also discuss some issues associated with computing Markov bases which are needed as an input to the algorithm. WIREs Comput Stat 2013, 5:207–218. doi: 10.1002/wics.1256This article is categorized under: Data: Types and Structure &gt; Traditional Statistical Data

Supporting incremental behaviour model elaboration

Behaviour model construction remains a difficult and labour intensive task which hinders the adoption of model-based methods by practitioners. We believe one reason for this is the mismatch between traditional approaches and current software development process best practices which include iterative development, adoption of use-case and scenario-based techniques and viewpoint- or stakeholder-based analysis; practices which require modelling and analysis in the presence of partial information about system behaviour. Our objective is to address the limitations of behaviour modelling and analysis by shifting the focus from traditional behaviour models and verification techniques that require full behaviour information to partial behaviour models and analysis techniques, that drive model elaboration rather than asserting adequacy. We aim to develop sound theory, techniques and tools that facilitate the construction of partial behaviour models through model synthesis, enable partial behaviour model analysis and provide feedback that prompts incremental elaboration of partial models. In this paper we present how the different research threads that we have and currently are developing help pursue this vision as part of the "Partial Behaviour Modelling--Foundations for Iterative Model Based Software Engineering" Starting Grant funded by the ERC. We cover partial behaviour modelling theory and construction, controller synthesis, automated diagnosis and refinement, and behaviour validation.

Learning Where to Attend with Deep Architectures for Image Tracking

We discuss an attentional model for simultaneous object tracking and recognition that is driven by gaze data. Motivated by theories of perception, the model consists of two interacting pathways, identity and control, intended to mirror the what and where pathways in neuroscience models. The identity pathway models object appearance and performs classification using deep (factored)-restricted Boltzmann machines. At each point in time, the observations consist of foveated images, with decaying resolution toward the periphery of the gaze. The control pathway models the location, orientation, scale, and speed of the attended object. The posterior distribution of these states is estimated with particle filtering. Deeper in the control pathway, we encounter an attentional mechanism that learns to select gazes so as to minimize tracking uncertainty. Unlike in our previous work, we introduce gaze selection strategies that operate in the presence of partial information and on a continuous action space. We show that a straightforward extension of the existing approach to the partial information setting results in poor performance, and we propose an alternative method based on modeling the reward surface as a gaussian process. This approach gives good performance in the presence of partial information and allows us to expand the action space from a small, discrete set of fixation points to a continuous domain.

Malliavin calculus applied to optimal control of stochastic partial differential equations with jumps

In this paper, we employ Malliavin calculus to derive a general stochastic maximum principle for stochastic partial differential equations with jumps under partial information. We apply this result to solve an optimal harvesting problem in the presence of partial information. Another application pertains to portfolio optimization under partial observation.

Risk indifference pricing of functional claims of the yield surface in the presence of partial information

In this paper we study the problem of risk indif- ference pricing of interest rate claims which are functionals of a bond yield surface under partial information. Our approach to solve this problem relies on a maximum principle for par- tial information control of stochastic dierential games based on generalized bond portfolios. The latter method enables us to establish an explicit representation of the risk indierence price of such claims.

A Generalized Logistic Item Response Model Parameterizing Test Score Inappropriateness

The person response curve has been suggested as a possible model for test score inappropriateness (Lums den, 1977, 1978; Weiss, 1973). The two-parameter person response curve proposed by Lumsden includes a person slope parameter but abandons the notion of differential item relatedness to the underlying trait. As an alternative, a generalized logistic model is consid ered that includes all item parameters of the three- parameter logistic model (Birnbaum, 1968). In addi tion to the usual person location parameter, the model has extra person parameters representing two possible characterizations of test score inappropriateness: a slope parameter indicating the degree to which a per son responds differently to items of varying difficulty, and an asymptote parameter measuring a person's pro clivity to engage in effective guessing or to omit items in the presence of partial information. To assess the model's feasibility, statistical comparisons were made between parameter estimates from data simulated ac cording to the model and the original simulation parameters. The results seem encouraging, but addi tional empirical study is needed before firm conclu sions can be drawn.