In congestion games, selfish users behave myopically to crowd to the shortest paths, and the social planner designs mechanisms to regulate such selfish routing through information or payment incentives. However, such mechanism design requires the knowledge of time-varying traffic conditions and it is the users themselves to learn and report past road experiences to the social planner (e.g., Waze or Google Maps). When congestion games meet mobile crowdsourcing, it is critical to incentivize selfish users to explore non-shortest paths in the best exploitation-exploration trade-off. First, we consider a simple but fundamental parallel routing network with one deterministic path and multiple stochastic paths for users with an average arrival probability $\lambda$. We prove that the current myopic routing policy (widely used in Waze and Google Maps) misses both exploration (when strong hazard belief) and exploitation (when weak hazard belief) as compared to the social optimum. Due to the myopic policy's under-exploration, we prove that the caused price of anarchy (PoA) is larger than \(\frac{1}{1-\rho^{\frac{1}{\lambda}}}\), which can be arbitrarily large as discount factor \(\rho\rightarrow1\). To mitigate such huge efficiency loss, we propose a novel selective information disclosure (SID) mechanism: we only reveal the latest traffic information to users when they intend to over-explore stochastic paths upon arrival, while hiding such information when they want to under-explore. We prove that our mechanism successfully reduces PoA to be less than~\(2\). Besides the parallel routing network, we further extend our mechanism and PoA results to any linear path graphs with multiple intermediate nodes.

We study the differences arising from merging predictors in the causal and anticausal directions using the same data. In particular we study the asymmetries that arise in a simple model where we merge the predictors using one binary variable as target and two continuous variables as predictors. We use Causal Maximum Entropy (CMAXENT) as inductive bias to merge the predictors, however, we expect similar differences to hold also when we use other merging methods that take into account asymmetries between cause and effect. We show that if we observe all bivariate distributions, the CMAXENT solution reduces to a logistic regression in the causal direction and Linear Discriminant Analysis (LDA) in the anticausal direction. Furthermore, we study how the decision boundaries of these two solutions differ whenever we observe only some of the bivariate distributions implications for Out-Of-Variable (OOV) generalisation.

Across the scientific realm, we find ourselves subtracting or dividing stochastic signals. For instance, consider a stochastic realization, $x$, generated from the addition or multiplication of two stochastic signals $a$ and $b$, namely $x=a+b$ or $x = ab$. For the $x=a+b$ example, $a$ can be fluorescence background and $b$ the signal of interest whose statistics are to be learned from the measured $x$. Similarly, when writing $x=ab$, $a$ can be thought of as the illumination intensity and $b$ the density of fluorescent molecules of interest. Yet dividing or subtracting stochastic signals amplifies noise, and we ask instead whether, using the statistics of $a$ and the measurement of $x$ as input, we can recover the statistics of $b$. Here, we show how normalizing flows can generate an approximation of the probability distribution over $b$, thereby avoiding subtraction or division altogether. This method is implemented in our software package, NFdeconvolve, available on GitHub with a tutorial linked in the main text.

This paper introduces a novel tree-based model, Learning Hyperplane Tree (LHT), which outperforms state-of-the-art (SOTA) tree models for classification tasks on several public datasets. The structure of LHT is simple and efficient: it partitions the data using several hyperplanes to progressively distinguish between target and non-target class samples. Although the separation is not perfect at each stage, LHT effectively improves the distinction through successive partitions. During testing, a sample is classified by evaluating the hyperplanes defined in the branching blocks and traversing down the tree until it reaches the corresponding leaf block. The class of the test sample is then determined using the piecewise linear membership function defined in the leaf blocks, which is derived through least-squares fitting and fuzzy logic. LHT is highly transparent and interpretable--at each branching block, the contribution of each feature to the classification can be clearly observed.

We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform the data into Gaussian random noise, and a backward SDE that gradually removes the noise to sample from the data distribution. By jointly training the two neural SDEs to minimize a common cost function that quantifies the difference between the two, the backward SDE converges to a diffusion process the starts with a Gaussian distribution and ends with the desired data distribution. Our method is closely related to normalizing flow and diffusion probabilistic models, and can be viewed as a combination of the two. Compared with normalizing flow, diffusion normalizing flow is able to learn distributions with sharp boundaries.

In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best known efficient algorithms for computing approximate PML distributions and improves when the number of distinct observed frequencies in the given instance is small. We achieve this result by exploiting new sparsity structure in approximate PML distributions and providing a new matrix rounding algorithm, of independent interest. Leveraging this result, we obtain the first provable computationally efficient implementation of PseudoPML, a general framework for estimating a broad class of symmetric properties. Additionally, we obtain efficient PML-based estimators for distributions with small profile entropy, a natural instance-based complexity measure.

Bayesian networks are a popular representation of asymmetric (for example causal) relationships between random variables. Markov random fields (MRFs) are a complementary model of symmetric relationships used in computer vision, spatial modeling, and social and gene expression networks. A chain graph model under the Lauritzen-Wermuth-Frydenberg interpretation (hereafter a chain graph model) generalizes both Bayesian networks and MRFs, and can represent asymmetric and symmetric relationships together.As in other graphical models, the set of marginals from distributions in a chain graph model induced by the presence of hidden variables forms a complex model. One recent approach to the study of marginal graphical models is to consider a well-behaved supermodel. Such a supermodel of marginals of Bayesian networks, defined only by conditional independences, and termed the ordinary Markov model, was studied at length in (Evans and Richardson, 2014).In this paper, we show that special mixed graphs which we call segregated graphs can be associated, via a Markov property, with supermodels of a marginal of chain graphs defined only by conditional independences.

Data assimilation (DA) is crucial for improving the accuracy of state estimation in complex dynamical systems by integrating observational data with physical models. Traditional solutions rely on either pure model-driven approaches, such as Bayesian filters that struggle with nonlinearity, or data-driven methods using deep learning priors, which often lack generalizability and physical interpretability. Recently, score-based DA methods have been introduced, focusing on learning prior distributions but neglecting explicit state transition dynamics, leading to limited accuracy improvements. To tackle the challenge, we introduce FlowDAS, a novel generative model-based framework using the stochastic interpolants to unify the learning of state transition dynamics and generative priors. FlowDAS achieves stable and observation-consistent inference by initializing from proximal previous states, mitigating the instability seen in score-based methods. Our extensive experiments demonstrate FlowDAS's superior performance on various benchmarks, from the Lorenz system to high-dimensional fluid super-resolution tasks. FlowDAS also demonstrates improved tracking accuracy on practical Particle Image Velocimetry (PIV) task, showcasing its effectiveness in complex flow field reconstruction.

We describe two Monte Carlo algorithms for sampling from the integrated posterior distributions of a range of Bayesian mixture models. Both algorithms allow us to directly sample not only the assignment of observations to components but also the number of components, thereby fitting the model and performing model selection over the number of components in a single computation. The first algorithm is a traditional collapsed Gibbs sampler, albeit with an unusual move-set; the second builds on the first, adding rejection-free sampling from the prior over component assignments, to create an algorithm that has excellent mixing time in typical applications and outperforms current state-of-the-art methods, in some cases by a wide margin. We demonstrate our methods with a selection of applications to latent class analysis.

This article discusses the integration of the Artificial Bee Colony (ABC) algorithm with two supervised learning methods, namely Artificial Neural Networks (ANNs) and Adaptive Network-based Fuzzy Inference System (ANFIS), for feature selection from Near-Infrared (NIR) spectra for predicting the molecular weight of medical-grade Polylactic Acid (PLA). During extrusion processing of PLA, in-line NIR spectra were captured along with extrusion process and machine setting data. With a dataset comprising 63 observations and 512 input features, appropriate machine learning tools are essential for interpreting data and selecting features to improve prediction accuracy. Initially, the ABC optimization algorithm is coupled with ANN/ANFIS to forecast PLA molecular weight. The objective functions of the ABC algorithm are to minimize the root mean square error (RMSE) between experimental and predicted PLA molecular weights while also minimizing the number of input features. Results indicate that employing ABC-ANFIS yields the lowest RMSE of 282 Da and identifies four significant parameters (NIR wavenumbers 6158 cm-1, 6310 cm-1, 6349 cm-1, and melt temperature) for prediction. These findings demonstrate the effectiveness of using the ABC algorithm with ANFIS for selecting a minimal set of features to predict PLA molecular weight with high accuracy during processing