Changes in the data distribution at test time can have deleterious effects on the performance of predictive models $p(y|x)$. We consider situations where there are additional meta-data labels (such as group labels), denoted by $z$, that can account for such changes in the distribution. In particular, we assume that the prior distribution $p(y, z)$, which models the dependence between the class label $y$ and the "nuisance" factors $z$, may change across domains, either due to a change in the correlation between these terms, or a change in one of their marginals. However, we assume that the generative model for features $p(x|y,z)$ is invariant across domains. We note that this corresponds to an expanded version of the widely used "label shift" assumption, where the labels now also include the nuisance factors $z$. Based on this observation, we propose a test-time label shift correction that adapts to changes in the joint distribution $p(y, z)$ using EM applied to unlabeled samples from the target domain distribution, $p_t(x)$. Importantly, we are able to avoid fitting a generative model $p(x|y, z)$, and merely need to reweight the outputs of a discriminative model $p_s(y, z|x)$ trained on the source distribution. We evaluate our method, which we call "Test-Time Label-Shift Adaptation" (TTLSA), on several standard image and text datasets, as well as the CheXpert chest X-ray dataset, and show that it improves performance over methods that target invariance to changes in the distribution, as well as baseline empirical risk minimization methods. Code for reproducing experiments is available at https://github.com/nalzok/test-time-label-shift .

Car-following (CF) algorithms are crucial components of traffic simulations and have been integrated into many production vehicles equipped with Advanced Driving Assistance Systems (ADAS). Insights from the model of car-following behavior help us understand the causes of various macro phenomena that arise from interactions between pairs of vehicles. Car-following models encompass multiple disciplines, including traffic engineering, physics, dynamic system control, cognitive science, machine learning, and reinforcement learning. This paper presents an extensive survey that highlights the differences, complementarities, and overlaps among microscopic traffic flow and control models based on their underlying principles and design logic. It reviews representative algorithms, ranging from theory-based kinematic models, Psycho-Physical Models, and Adaptive cruise control models to data-driven algorithms like Reinforcement Learning and Imitation Learning (IL). The manuscript discusses the strengths and limitations of these models and explores their applications in different contexts. This review synthesizes existing researches across different domains to fill knowledge gaps and offer guidance for future research by identifying the latest trends in car following models and their applications.

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for performance on average is intuitive, convenient to analyze in theory, and easy to implement in practice, such a choice brings about trade-offs. In this work, we survey and introduce a wide variety of non-traditional criteria used to design and evaluate machine learning algorithms, place the classical paradigm within the proper historical context, and propose a view of learning problems which emphasizes the question of "what makes for a desirable loss distribution?" in place of tacit use of the expected loss.

It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important properties of the model in the large data limit, including the rate of convergence of the conditional mean to the response function. We prove that the maximum likelihood estimate of the smoothness parameter cannot asymptotically undersmooth the truth when the data are obtained on a fixed bounded subset of $\mathbb{R}^d$. That is, if the data-generating response function has Sobolev smoothness $\nu_0 > d/2$, then the smoothness parameter estimate cannot be asymptotically less than $\nu_0$. The lower bound is sharp. Additionally, we show that maximum likelihood estimation recovers the true smoothness for a class of compactly supported self-similar functions. For cross-validation we prove an asymptotic lower bound $\nu_0 - d/2$, which however is unlikely to be sharp. The results are based on approximation theory in Sobolev spaces and some general theorems that restrict the set of values that the parameter estimators can take.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

In this work, we address the challenge of multi-task image generation with limited data for denoising diffusion probabilistic models (DDPM), a class of generative models that produce high-quality images by reversing a noisy diffusion process. We propose a novel method, SR-DDPM, that leverages representation-based techniques from few-shot learning to effectively learn from fewer samples across different tasks. Our method consists of a core meta architecture with shared parameters, i.e., task-specific layers with exclusive parameters. By exploiting the similarity between diverse data distributions, our method can scale to multiple tasks without compromising the image quality. We evaluate our method on standard image datasets and show that it outperforms both unconditional and conditional DDPM in terms of FID and SSIM metrics.

We reinvigorate maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our architecture features several key ingredients making MLE work in this context. First, the hemispheres share a common core at the entrance of the network which accommodates for various forms of time variation in the error variance. Second, we introduce a volatility emphasis constraint that breaks mean/variance indeterminacy in this class of overparametrized nonlinear models. Third, we conduct a blocked out-of-bag reality check to curb overfitting in both conditional moments. Fourth, the algorithm utilizes standard deep learning software and thus handles large data sets - both computationally and statistically. Ergo, our Hemisphere Neural Network (HNN) provides proactive volatility forecasts based on leading indicators when it can, and reactive volatility based on the magnitude of previous prediction errors when it must. We evaluate point and density forecasts with an extensive out-of-sample experiment and benchmark against a suite of models ranging from classics to more modern machine learning-based offerings. In all cases, HNN fares well by consistently providing accurate mean/variance forecasts for all targets and horizons. Studying the resulting volatility paths reveals its versatility, while probabilistic forecasting evaluation metrics showcase its enviable reliability. Finally, we also demonstrate how this machinery can be merged with other structured deep learning models by revisiting Goulet Coulombe (2022)'s Neural Phillips Curve.

In this paper, a new method based on TOPSIS and optimization models is proposed for multi-attribute group decision-making in the environment of interval-valued intuitionistic fuzzy sets.Firstly, by minimizing the sum of differences between individual evaluations and the overallconsistent evaluations of all experts, a new optimization model is established for determining expert weights. Secondly, based on TOPSIS method, the improved closeness index for evaluating each alternative is obtained. Finally, the attribute weight is determined by establishing an optimization model with the goal of maximizing the closeness of each alternative, and it is brought into the closeness index so that the alternatives can be ranked. Combining all these together, the complete fuzzy multi-attribute group decision-making algorithm is formulated, which can give full play to the advantages of subjective and objective weighting methods. In the end, the feasibility and effectiveness of the provided method are verified by a real case study.

Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

Federated learning is a new learning paradigm that decouples data collection and model training via multi-party computation and model aggregation. As a flexible learning setting, federated learning has the potential to integrate with other learning frameworks. We conduct a focused survey of federated learning in conjunction with other learning algorithms. Specifically, we explore various learning algorithms to improve the vanilla federated averaging algorithm and review model fusion methods such as adaptive aggregation, regularization, clustered methods, and Bayesian methods. Following the emerging trends, we also discuss federated learning in the intersection with other learning paradigms, termed federated X learning, where X includes multitask learning, meta-learning, transfer learning, unsupervised learning, and reinforcement learning. This survey reviews the state of the art, challenges, and future directions.