We present the first calibration of quantum decision theory (QDT) to a dataset of binary risky choice. We quantitatively account for the fraction of choice reversals between two repetitions of the experiment, using a probabilistic choice formulation in the simplest form without model assumption or adjustable parameters. The prediction of choice reversal is then refined by introducing heterogeneity between decision makers through their differentiation into two groups: ``majoritarian'' and ``contrarian'' (in proportion 3:1). This supports the first fundamental tenet of QDT, which models choice as an inherent probabilistic process, where the probability of a prospect can be expressed as the sum of its utility and attraction factors. We propose to parameterise the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and the attraction factor with a constant absolute risk aversion (CARA) function. For this dataset, and penalising the larger number of QDT parameters via the Wilks test of nested hypotheses, the QDT model is found to perform significantly better than logit-CPT at both the aggregate and individual levels, and for all considered fit criteria for the first experiment iteration and for predictions (second ``out-of-sample'' iteration). The distinctive QDT effect captured by the attraction factor is mostly appreciable (i.e., most relevant and strongest in amplitude) for prospects with big losses. Our quantitative analysis of the experimental results supports the existence of an intrinsic limit of predictability, which is associated with the inherent probabilistic nature of choice. The results of the paper can find applications both in the prediction of choice of human decision makers as well as for organizing the operation of artificial intelligence.
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Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. A well-known limitation of IRL is the ambiguity in the choice of the reward function, due to the existence of multiple rewards that explain the observed behavior. This limitation has been recently circumvented by formulating IRL as the problem of estimating the feasible reward set, i.e., the region of the rewards compatible with the expert's behavior. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model. We start by formally introducing the problem of estimating the feasible reward set, the corresponding PAC requirement, and discussing the properties of particular classes of rewards. Then, we provide the first minimax lower bound on the sample complexity for the problem of estimating the feasible reward set of order ${\Omega}\Bigl( \frac{H^3SA}{\epsilon^2} \bigl( \log \bigl(\frac{1}{\delta}\bigl) + S \bigl)\Bigl)$, being $S$ and $A$ the number of states and actions respectively, $H$ the horizon, $\epsilon$ the desired accuracy, and $\delta$ the confidence. We analyze the sample complexity of a uniform sampling strategy (US-IRL), proving a matching upper bound up to logarithmic factors. Finally, we outline several open questions in IRL and propose future research directions.
Graph neural networks (GNNs) are widely used for modeling complex interactions between entities represented as vertices of a graph. Despite recent efforts to theoretically analyze the expressive power of GNNs, a formal characterization of their ability to model interactions is lacking. The current paper aims to address this gap. Formalizing strength of interactions through an established measure known as separation rank, we quantify the ability of certain GNNs to model interaction between a given subset of vertices and its complement, i.e. between the sides of a given partition of input vertices. Our results reveal that the ability to model interaction is primarily determined by the partition's walk index -- a graph-theoretical characteristic defined by the number of walks originating from the boundary of the partition. Experiments with common GNN architectures corroborate this finding. As a practical application of our theory, we design an edge sparsification algorithm named Walk Index Sparsification (WIS), which preserves the ability of a GNN to model interactions when input edges are removed. WIS is simple, computationally efficient, and in our experiments has markedly outperformed alternative methods in terms of induced prediction accuracy. More broadly, it showcases the potential of improving GNNs by theoretically analyzing the interactions they can model.
To make accurate inferences in an interactive setting, an agent must not confuse passive observation of events with having intervened to cause them. The $do$ operator formalises interventions so that we may reason about their effect. Yet there exist pareto optimal mathematical formalisms of general intelligence in an interactive setting which, presupposing no explicit representation of intervention, make maximally accurate inferences. We examine one such formalism. We show that in the absence of a $do$ operator, an intervention can be represented by a variable. We then argue that variables are abstractions, and that need to explicitly represent interventions in advance arises only because we presuppose these sorts of abstractions. The aforementioned formalism avoids this and so, initial conditions permitting, representations of relevant causal interventions will emerge through induction. These emergent abstractions function as representations of one`s self and of any other object, inasmuch as the interventions of those objects impact the satisfaction of goals. We argue that this explains how one might reason about one`s own identity and intent, those of others, of one`s own as perceived by others and so on. In a narrow sense this describes what it is to be aware, and is a mechanistic explanation of aspects of consciousness.
Bayesian Additive Regression Trees (BART) are a powerful semiparametric ensemble learning technique for modeling nonlinear regression functions. Although initially BART was proposed for predicting only continuous and binary response variables, over the years multiple extensions have emerged that are suitable for estimating a wider class of response variables (e.g. categorical and count data) in a multitude of application areas. In this paper we describe a Generalized framework for Bayesian trees and their additive ensembles where the response variable comes from an exponential family distribution and hence encompasses a majority of these variants of BART. We derive sufficient conditions on the response distribution, under which the posterior concentrates at a minimax rate, up to a logarithmic factor. In this regard our results provide theoretical justification for the empirical success of BART and its variants.
In many recommender systems and search problems, presenting a well balanced set of results can be an important goal in addition to serving highly relevant content. For example, in a movie recommendation system, it may be helpful to achieve a certain balance of different genres, likewise, it may be important to balance between highly popular versus highly personalized shows. Such balances could be thought across many categories and may be required for enhanced user experience, business considerations, fairness objectives etc. In this paper, we consider the problem of calibrating with respect to any given categories over items. We propose a way to balance a trade-off between relevance and calibration via a Linear Programming optimization problem where we learn a doubly stochastic matrix to achieve optimal balance in expectation. We then realize the learned policy using the Birkhoff-von Neumann decomposition of a doubly stochastic matrix. Several optimizations are considered over the proposed basic approach to make it fast. The experiments show that the proposed formulation can achieve a much better trade-off compared to many other baselines. This paper does not prescribe the exact categories to calibrate over (such as genres) universally for applications. This is likely dependent on the particular task or business objective. The main contribution of the paper is that it proposes a framework that can be applied to a variety of problems and demonstrates the efficacy of the proposed method using a few use-cases.
Electricity load forecasting is a necessary capability for power system operators and electricity market participants. The proliferation of local generation, demand response, and electrification of heat and transport are changing the fundamental drivers of electricity load and increasing the complexity of load modelling and forecasting. We address this challenge in two ways. First, our setting is adaptive; our models take into account the most recent observations available, yielding a forecasting strategy able to automatically respond to changes in the underlying process. Second, we consider probabilistic rather than point forecasting; indeed, uncertainty quantification is required to operate electricity systems efficiently and reliably. Our methodology relies on the Kalman filter, previously used successfully for adaptive point load forecasting. The probabilistic forecasts are obtained by quantile regressions on the residuals of the point forecasting model. We achieve adaptive quantile regressions using the online gradient descent; we avoid the choice of the gradient step size considering multiple learning rates and aggregation of experts. We apply the method to two data sets: the regional net-load in Great Britain and the demand of seven large cities in the United States. Adaptive procedures improve forecast performance substantially in both use cases for both point and probabilistic forecasting.
Cooperative perception is a promising technique for enhancing the perception capabilities of automated vehicles through vehicle-to-everything (V2X) cooperation, provided that accurate relative pose transforms are available. Nevertheless, obtaining precise positioning information often entails high costs associated with navigation systems. Moreover, signal drift resulting from factors such as occlusion and multipath effects can compromise the stability of the positioning information. Hence, a low-cost and robust method is required to calibrate relative pose information for multi-agent cooperative perception. In this paper, we propose a simple but effective inter-agent object association approach (CBM), which constructs contexts using the detected bounding boxes, followed by local context matching and global consensus maximization. Based on the matched correspondences, optimal relative pose transform is estimated, followed by cooperative perception fusion. Extensive experimental studies are conducted on both the simulated and real-world datasets, high object association precision and decimeter level relative pose calibration accuracy is achieved among the cooperating agents even with larger inter-agent localization errors. Furthermore, the proposed approach outperforms the state-of-the-art methods in terms of object association and relative pose estimation accuracy, as well as the robustness of cooperative perception against the pose errors of the connected agents. The code will be available at //github.com/zhyingS/CBM.
The capability of Large Language Models (LLMs) like ChatGPT to comprehend user intent and provide reasonable responses has made them extremely popular lately. In this paper, we focus on assessing the overall ability of ChatGPT using 7 fine-grained information extraction (IE) tasks. Specially, we present the systematically analysis by measuring ChatGPT's performance, explainability, calibration, and faithfulness, and resulting in 15 keys from either the ChatGPT or domain experts. Our findings reveal that ChatGPT's performance in Standard-IE setting is poor, but it surprisingly exhibits excellent performance in the OpenIE setting, as evidenced by human evaluation. In addition, our research indicates that ChatGPT provides high-quality and trustworthy explanations for its decisions. However, there is an issue of ChatGPT being overconfident in its predictions, which resulting in low calibration. Furthermore, ChatGPT demonstrates a high level of faithfulness to the original text in the majority of cases. We manually annotate and release the test sets of 7 fine-grained IE tasks contains 14 datasets to further promote the research. The datasets and code are available at //github.com/pkuserc/ChatGPT_for_IE.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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