Neural point estimators are neural networks that map data to parameter point estimates. They are fast, likelihood free and, due to their amortised nature, amenable to fast bootstrap-based uncertainty quantification. In this paper, we aim to increase the awareness of statisticians to this relatively new inferential tool, and to facilitate its adoption by providing user-friendly open-source software. We also give attention to the ubiquitous problem of making inference from replicated data, which we address in the neural setting using permutation-invariant neural networks. Through extensive simulation studies we show that these neural point estimators can quickly and optimally (in a Bayes sense) estimate parameters in weakly-identified and highly-parameterised models with relative ease. We demonstrate their applicability through an analysis of extreme sea-surface temperature in the Red Sea where, after training, we obtain parameter estimates and bootstrap-based confidence intervals from hundreds of spatial fields in a fraction of a second.

Few-shot learning is valuable in many real-world applications, but learning a generalizable model without overfitting to the few labeled datapoints is challenging. In this work, we focus on Few-shot Learning with Auxiliary Data (FLAD), a training paradigm that assumes access to auxiliary data during few-shot learning in hopes of improving generalization. Previous works have proposed automated methods for mixing auxiliary and target data, but these methods typically scale linearly (or worse) with the number of auxiliary datasets, limiting their practicality. In this work we relate FLAD to the explore-exploit dilemma that is central to the multi-armed bandit setting and derive algorithms whose computational complexity is independent of the number of auxiliary datasets, allowing us to scale to 100 more auxiliary datasets than prior methods. We propose two algorithms - EXP3-FLAD and UCB1-FLAD - and compare them with prior FLAD methods that either explore or exploit, finding that the combination of exploration and exploitation is crucial. Through extensive experimentation we find that our methods outperform all pre-existing FLAD methods by 4% and lead to the first 3 billion parameter language models that outperform the 175 billion parameter GPT-3. Overall, our work suggests that the discovery of better, more efficient mixing strategies for FLAD may provide a viable path towards substantially improving generalization in few-shot learning. All of our code is available at github.com/alon-albalak/FLAD.

Financial markets play a pivotal role in global economic activities, and their operations and dynamic evolutions are intricately linked to a myriad of chaotic and complex factors, including economic configurations, seasonal components, and the international milieu [1] [2]. As the economy progresses and financial markets expand continuously, time series analysis in finance has become indispensable [3]. This analytical approach has significantly advanced the understanding of market dynamics, refined intelligent decision-making processes, and bolstered developments in forecasting investment returns [4][2]. Consequently, it has garnered immense scholarly attention, leading to abundant research contributions in this domain. In stark contrast to conventional time series prediction endeavors characterizing various scientific domains--such as the temporal allocation mechanisms associated with wind energy integration [5], the granular analysis of protracted energy consumption patterns in architectural structures [6], or the intricate forecasting of load dynamics within thermal frameworks [7]--the sphere of financial time series forecasting is imbued with an elevated level of complexity and unpredictability.

In the present research, we delve into the intricate realm of electroencephalogram (EEG) data analysis, focusing on sequence-to-sequence prediction of data across 32 EEG channels. The study harmoniously fuses the principles of applied chaos theory and dynamical systems theory to engender a novel feature set, enriching the representational capacity of our deep learning model. The endeavour's cornerstone is a transformer-based sequence-to-sequence architecture, calibrated meticulously to capture the non-linear and high-dimensional temporal dependencies inherent in EEG sequences. Through judicious architecture design, parameter initialisation strategies, and optimisation techniques, we have navigated the intricate balance between computational expediency and predictive performance. Our model stands as a vanguard in EEG data sequence prediction, demonstrating remarkable generalisability and robustness. The findings not only extend our understanding of EEG data dynamics but also unveil a potent analytical framework that can be adapted to diverse temporal sequence prediction tasks in neuroscience and beyond.

High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented na\"ively, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. Using similar ideas, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods.

We propose Joint MLP/Attention (JoMA) dynamics, a novel mathematical framework to understand the training procedure of multilayer Transformer architectures. This is achieved by integrating out the self-attention layer in Transformers, producing a modified dynamics of MLP layers only. JoMA removes unrealistic assumptions in previous analysis (e.g., lack of residual connection) and predicts that the attention first becomes sparse (to learn salient tokens), then dense (to learn less salient tokens) in the presence of nonlinear activations, while in the linear case, it is consistent with existing works that show attention becomes sparse over time. We leverage JoMA to qualitatively explains how tokens are combined to form hierarchies in multilayer Transformers, when the input tokens are generated by a latent hierarchical generative model. Experiments on models trained from real-world dataset (Wikitext2/Wikitext103) and various pre-trained models (OPT, Pythia) verify our theoretical findings.

AI has greatly enhanced medical image analysis, yet its use in epidemiological population imaging studies remains limited due to visualization challenges in non-linear models and lack of confounder control. Addressing this, we introduce an AI method emphasizing semantic feature interpretation and resilience against multiple confounders. Our approach's merits are tested in three scenarios: extracting confounder-free features from a 2D synthetic dataset; examining the association between prenatal alcohol exposure and children's facial shapes using 3D mesh data; exploring the relationship between global cognition and brain images with a 3D MRI dataset. Results confirm our method effectively reduces confounder influences, establishing less confounded associations. Additionally, it provides a unique visual representation, highlighting specific image alterations due to identified correlations.

Conditional stochastic optimization has found applications in a wide range of machine learning tasks, such as invariant learning, AUPRC maximization, and meta-learning. As the demand for training models with large-scale distributed data grows in these applications, there is an increasing need for communication-efficient distributed optimization algorithms, such as federated learning algorithms. This paper considers the nonconvex conditional stochastic optimization in federated learning and proposes the first federated conditional stochastic optimization algorithm (FCSG) with a conditional stochastic gradient estimator and a momentum-based algorithm (FCSG-M). To match the lower bound complexity in the single-machine setting, we design an accelerated algorithm (Acc-FCSG-M) via the variance reduction to achieve the best sample and communication complexity. Compared with the existing optimization analysis for MAML in FL, federated conditional stochastic optimization considers the sample of tasks. Extensive experimental results on various tasks validate the efficiency of these algorithms.

Mainstream navigation software, like Google and Apple Maps, often lacks the ability to provide routes prioritizing safety. However, safety remains a paramount concern for many. Our aim is to strike a balance between safety and efficiency. To achieve this, we're devising an Integer Programming model that takes into account both the shortest path and the safest route. We will harness machine learning to derive safety coefficients, employing methodologies such as generalized linear models, linear regression, and recurrent neural networks. Our evaluation will be based on the Root Mean Square Error (RMSE) across various subway stations, helping us identify the most accurate model for safety coefficient estimation. Furthermore, we'll conduct a comprehensive review of different shortest-path algorithms, assessing them based on time complexity and real-world data to determine their appropriateness in merging both safety and time efficiency.

Given the growing prevalence of diabetes, there has been significant interest in determining how diabetes affects instrumental daily functions, like driving. Complication of glucose control in diabetes includes hypoglycemic and hyperglycemic episodes, which may impair cognitive and psychomotor functions needed for safe driving. The goal of this paper was to determine patterns of diabetes speed behavior during acute glucose to drivers with diabetes who were euglycemic or control drivers without diabetes in a naturalistic driving environment. By employing distribution-based analytic methods which capture distribution patterns, our study advances prior literature that has focused on conventional approach of average speed to explore speed deviation patterns.