This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can, however, be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020s, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, by representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modeling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.

Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in such interactive settings. However, tractable algorithms for such problems usually rely on a strong assumption, namely that the objectives of all players in the scene are known. To make such tools applicable for ego-centric planning with only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' objectives online and computes a corresponding generalized Nash equilibrium (GNE) strategy. The adaptivity of our approach is enabled by a differentiable trajectory game solver whose gradient signal is used for maximum likelihood estimation (MLE) of opponents' objectives. This differentiability of our pipeline facilitates direct integration with other differentiable elements, such as neural networks (NNs). Furthermore, in contrast to existing solvers for cost inference in games, our method handles not only partial state observations but also general inequality constraints. In two simulated traffic scenarios, we find superior performance of our approach over both existing game-theoretic methods and non-game-theoretic model-predictive control (MPC) approaches. We also demonstrate our approach's real-time planning capabilities and robustness in two hardware experiments.

Access to complete data in large-scale networks is often infeasible. Therefore, the problem of missing data is a crucial and unavoidable issue in the analysis and modeling of real-world social networks. However, most of the research on different aspects of social networks does not consider this limitation. One effective way to solve this problem is to recover the missing data as a pre-processing step. In this paper, a model is learned from partially observed data to infer unobserved diffusion and structure networks. To jointly discover omitted diffusion activities and hidden network structures, we develop a probabilistic generative model called "DiffStru." The interrelations among links of nodes and cascade processes are utilized in the proposed method via learning coupled with low-dimensional latent factors. Besides inferring unseen data, latent factors such as community detection may also aid in network classification problems. We tested different missing data scenarios on simulated independent cascades over LFR networks and real datasets, including Twitter and Memtracker. Experiments on these synthetic and real-world datasets show that the proposed method successfully detects invisible social behaviors, predicts links, and identifies latent features.

Latent confounding has been a long-standing obstacle for causal reasoning from observational data. One popular approach is to model the data using acyclic directed mixed graphs (ADMGs), which describe ancestral relations between variables using directed and bidirected edges. However, existing methods using ADMGs are based on either linear functional assumptions or a discrete search that is complicated to use and lacks computational tractability for large datasets. In this work, we further extend the existing body of work and develop a novel gradient-based approach to learning an ADMG with non-linear functional relations from observational data. We first show that the presence of latent confounding is identifiable under the assumptions of bow-free ADMGs with non-linear additive noise models. With this insight, we propose a novel neural causal model based on autoregressive flows for ADMG learning. This not only enables us to determine complex causal structural relationships behind the data in the presence of latent confounding, but also estimate their functional relationships (hence treatment effects) simultaneously. We further validate our approach via experiments on both synthetic and real-world datasets, and demonstrate the competitive performance against relevant baselines.

Conditional Neural Processes~(CNPs) formulate distributions over functions and generate function observations with exact conditional likelihoods. CNPs, however, have limited expressivity for high-dimensional observations, since their predictive distribution is factorized into a product of unconstrained (typically) Gaussian outputs. Previously, this could be handled using latent variables or autoregressive likelihood, but at the expense of intractable training and quadratically increased complexity. Instead, we propose calibrating CNPs with an adversarial training scheme besides regular maximum likelihood estimates. Specifically, we train an energy-based model (EBM) with noise contrastive estimation, which enforces EBM to identify true observations from the generations of CNP. In this way, CNP must generate predictions closer to the ground-truth to fool EBM, instead of merely optimizing with respect to the fixed-form likelihood. From generative function reconstruction to downstream regression and classification tasks, we demonstrate that our method fits mainstream CNP members, showing effectiveness when unconstrained Gaussian likelihood is defined, requiring minimal computation overhead while preserving foundation properties of CNPs.

This article is written for pedagogical purposes aiming at practitioners trying to estimate the finite support of continuous probability distributions, i.e., the minimum and the maximum of a distribution defined on a finite domain. Generalized Pareto distribution GP({\theta}, {\sigma}, {\xi}) is a three-parameter distribution which plays a key role in Peaks-Over-Threshold framework for tail estimation in Extreme Value Theory. Estimators for GP often lack analytical solutions and the best known Bayesian methods for GP involves numerical methods. Moreover, existing literature focuses on estimating the scale {\sigma} and the shape {\xi}, lacking discussion of the estimation of the location {\theta} which is the lower support of (minimum value possible in) a GP. To fill the gap, we analyze four two-parameter subclasses of GP whose conjugate priors can be obtained analytically, although some of the results are known. Namely, we prove the conjugacy for {\xi} > 0 (Pareto), {\xi} = 0 (Shifted Exponential), {\xi} < 0 (Power), and {\xi} = -1 (Two-parameter Uniform).

When considering an invariant that gives a Bayesian generalization error, that is a real log canonical threshold, in general, papers replace a mean error function with a relatively simple polynomial whose real log canonical threshold corresponds to that of the mean error function, and obtain its real log canonical threshold by resolving its singularities through an algebraic operation called blow-up. Though it is known that the singularities of any polynomial can be resolved by a finite number of blow-up iterations, it is not clarified well whether or not it is possible to resolve singularities of a specific polynomial by applying a specific blow-up algorithm. Therefore this paper proposes a blow-up algorithm that can be applied to the polynomials called sum-of-products polynomials and proves that it halts. Furthermore, this paper considers real log canonical thresholds of sum-of-products polynomials by using the algorithm. First, this section explains the foundation of Bayesian learning theory and details the relation to a real log canonical threshold and blow-up. Then this section defines exclusive sum-of-products polynomials which is subject to previous studies and explains the novelty and utility of this paper.

An algorithm based on a deep probabilistic architecture referred to as a tree-structured sum-product network (t-SPN) is considered for cell classification. The t-SPN is constructed such that the unnormalized probability is represented as conditional probabilities of a subset of most similar cell classes. The constructed t-SPN architecture is learned by maximizing the margin, which is the difference in the conditional probability between the true and the most competitive false label. To enhance the generalization ability of the architecture, L2-regularization (REG) is considered along with the maximum margin (MM) criterion in the learning process. To highlight cell features, this paper investigates the effectiveness of two generic high-pass filters: ideal high-pass filtering and the Laplacian of Gaussian (LOG) filtering. On both HEp-2 and Feulgen benchmark datasets, the t-SPN architecture learned based on the max-margin criterion with regularization produced the highest accuracy rate compared to other state-of-the-art algorithms that include convolutional neural network (CNN) based algorithms. The ideal high-pass filter was more effective on the HEp-2 dataset, which is based on immunofluorescence staining, while the LOG was more effective on the Feulgen dataset, which is based on Feulgen staining.

We propose a new general model called IPNN - Indeterminate Probability Neural Network, which combines neural network and probability theory together. In the classical probability theory, the calculation of probability is based on the occurrence of events, which is hardly used in current neural networks. In this paper, we propose a new general probability theory, which is an extension of classical probability theory, and makes classical probability theory a special case to our theory. Besides, for our proposed neural network framework, the output of neural network is defined as probability events, and based on the statistical analysis of these events, the inference model for classification task is deduced. IPNN shows new property: It can perform unsupervised clustering while doing classification. Besides, IPNN is capable of making very large classification with very small neural network, e.g. model with 100 output nodes can classify 10 billion categories. Theoretical advantages are reflected in experimental results.

Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are largely heuristic and depend heavily on empirical results, lacking theoretical explanation. Furthermore, existing methods overlook the decision loss, which characterizes different costs associated with tailed classes. This paper presents a general and principled framework from a Bayesian-decision-theory perspective, which unifies existing techniques including re-balancing and ensemble methods, and provides theoretical justifications for their effectiveness. From this perspective, we derive a novel objective based on the integrated risk and a Bayesian deep-ensemble approach to improve the accuracy of all classes, especially the "tail". Besides, our framework allows for task-adaptive decision loss which provides provably optimal decisions in varying task scenarios, along with the capability to quantify uncertainty. Finally, We conduct comprehensive experiments, including standard classification, tail-sensitive classification with a new False Head Rate metric, calibration, and ablation studies. Our framework significantly improves the current SOTA even on large-scale real-world datasets like ImageNet.