Widely Linear vs. Conventional Subspace-Based Estimation of SIMO Flat-Fading Channels: Mean-Squared Error Analysis

We analyze the mean-squared error (MSE) performance of widely linear (WL) and conventional subspace-based channel estimation for single-input multiple-output (SIMO) flat-fading channels employing binary phase-shift-keying (BPSK) modulation when the covariance matrix is estimated using a finite number of samples. The conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the WL estimator. We derive closed-form expressions for the MSE of the two estimators under four different ambiguity resolution scenarios. The first scenario is optimal resolution, which minimizes the Euclidean distance between the channel estimate and the actual channel. The second scenario assumes that a randomly chosen coefficient of the actual channel is known and the third assumes that the one with the largest magnitude is known. The fourth scenario is the more realistic case where pilot symbols are used to resolve the ambiguities. Our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of WL and conventional subspace-based estimators, and shows that the less information available about the actual channel for ambiguity resolution, or the lower the accuracy of this information, the higher the performance gap in favor of the WL estimator.Comment: 20 pages, 7 figure

Multi-Context Models for Reasoning under Partial Knowledge: Generative Process and Inference Grammar

Arriving at the complete probabilistic knowledge of a domain, i.e., learning how all variables interact, is indeed a demanding task. In reality, settings often arise for which an individual merely possesses partial knowledge of the domain, and yet, is expected to give adequate answers to a variety of posed queries. That is, although precise answers to some queries, in principle, cannot be achieved, a range of plausible answers is attainable for each query given the available partial knowledge. In this paper, we propose the Multi-Context Model (MCM), a new graphical model to represent the state of partial knowledge as to a domain. MCM is a middle ground between Probabilistic Logic, Bayesian Logic, and Probabilistic Graphical Models. For this model we discuss: (i) the dynamics of constructing a contradiction-free MCM, i.e., to form partial beliefs regarding a domain in a gradual and probabilistically consistent way, and (ii) how to perform inference, i.e., to evaluate a probability of interest involving some variables of the domain.Comment: To appear in the Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence (UAI 2015

A Rational Distributed Process-level Account of Independence Judgment

It is inconceivable how chaotic the world would look to humans, faced with innumerable decisions a day to be made under uncertainty, had they been lacking the capacity to distinguish the relevant from the irrelevant---a capacity which computationally amounts to handling probabilistic independence relations. The highly parallel and distributed computational machinery of the brain suggests that a satisfying process-level account of human independence judgment should also mimic these features. In this work, we present the first rational, distributed, message-passing, process-level account of independence judgment, called $\mathcal{D}^\ast$. Interestingly, $\mathcal{D}^\ast$ shows a curious, but normatively-justified tendency for quick detection of dependencies, whenever they hold. Furthermore, $\mathcal{D}^\ast$ outperforms all the previously proposed algorithms in the AI literature in terms of worst-case running time, and a salient aspect of it is supported by recent work in neuroscience investigating possible implementations of Bayes nets at the neural level. $\mathcal{D}^\ast$ nicely exemplifies how the pursuit of cognitive plausibility can lead to the discovery of state-of-the-art algorithms with appealing properties, and its simplicity makes $\mathcal{D}^\ast$ potentially a good candidate for pedagogical purposes

The Causal Frame Problem: An Algorithmic Perspective

The Frame Problem (FP) is a puzzle in philosophy of mindand epistemology, articulated by the Stanford Encyclopedia ofPhilosophy as follows: “How do we account for our apparentability to make decisions on the basis only of what is relevantto an ongoing situation without having explicitly to considerall that is not relevant?” In this work, we focus on the causalvariant of the FP, the Causal Frame Problem (CFP). Assumingthat a reasoner’s mental causal model can be (implicitly) repre-sented by a causal Bayes net, we first introduce a notion calledPotential Level (PL). PL, in essence, encodes the relative po-sition of a node with respect to its neighbors in a causal Bayesnet. Drawing on the psychological literature on causal judg-ment, we substantiate the claim that PL may bear on how timeis encoded in the mind. Using PL, we propose an inferenceframework, called the PL-based Inference Framework (PLIF),which permits a boundedly-rational approach to the CFP, for-mally articulated at Marr’s algorithmic level of analysis. Weshow that our proposed framework, PLIF, is consistent withseveral findings in the causal judgment literature, and that PLand PLIF make a number of predictions, some of which arealready supported by existing findings

The Causal Frame Problem: An Algorithmic Perspective

The Frame Problem (FP) is a puzzle in philosophy of mindand epistemology, articulated by the Stanford Encyclopedia ofPhilosophy as follows: “How do we account for our apparentability to make decisions on the basis only of what is relevantto an ongoing situation without having explicitly to considerall that is not relevant?” In this work, we focus on the causalvariant of the FP, the Causal Frame Problem (CFP). Assumingthat a reasoner’s mental causal model can be (implicitly) repre-sented by a causal Bayes net, we first introduce a notion calledPotential Level (PL). PL, in essence, encodes the relative po-sition of a node with respect to its neighbors in a causal Bayesnet. Drawing on the psychological literature on causal judg-ment, we substantiate the claim that PL may bear on how timeis encoded in the mind. Using PL, we propose an inferenceframework, called the PL-based Inference Framework (PLIF),which permits a boundedly-rational approach to the CFP, for-mally articulated at Marr’s algorithmic level of analysis. Weshow that our proposed framework, PLIF, is consistent withseveral findings in the causal judgment literature, and that PLand PLIF make a number of predictions, some of which arealready supported by existing findings