The signature kernel is a kernel between time series of arbitrary length and comes with strong theoretical guarantees from stochastic analysis. It has found applications in machine learning such as covariance functions for Gaussian processes. A strength of the underlying signature features is that they provide a structured global description of a time series. However, this property can quickly become a curse when local information is essential and forgetting is required; so far this has only been addressed with ad-hoc methods such as slicing the time series into subsegments. To overcome this, we propose a principled, data-driven approach by introducing a novel forgetting mechanism for signatures. This allows the model to dynamically adapt its context length to focus on more recent information. To achieve this, we revisit the recently introduced Random Fourier Signature Features, and develop Random Fourier Decayed Signature Features (RFDSF) with Gaussian processes (GPs). This results in a Bayesian time series forecasting algorithm with variational inference, that offers a scalable probabilistic algorithm that processes and transforms a time series into a joint predictive distribution over time steps in one pass using recurrence. For example, processing a sequence of length $10^4$ steps in $\approx 10^{-2}$ seconds and in $< 1\text{GB}$ of GPU memory. We demonstrate that it outperforms other GP-based alternatives and competes with state-of-the-art probabilistic time series forecasting algorithms.

When estimating heterogeneous treatment effects, missing outcome data can complicate treatment effect estimation, causing certain subgroups of the population to be poorly represented. In this work, we discuss this commonly overlooked problem and consider the impact that missing at random (MAR) outcome data has on causal machine learning estimators for the conditional average treatment effect (CATE). We then propose two de-biased machine learning estimators for the CATE, the mDR-learner and mEP-learner, which address the issue of under-representation by integrating inverse probability of censoring weights into the DR-learner and EP-learner respectively. We show that under reasonable conditions, these estimators are oracle efficient, and illustrate their favorable performance through simulated data settings, comparing them to existing CATE estimators, including comparison to estimators which use common missing data techniques. Guidance on the implementation of these estimators is provided and we present an example of their application using the ACTG175 trial, exploring treatment effect heterogeneity when comparing Zidovudine mono-therapy against alternative antiretroviral therapies among HIV-1-infected individuals.

Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the stochastic noise (the difference between the stochastic and true gradient) is considered only to have a finite $\mathfrak{p}$-th moment where $\mathfrak{p}\in\left(1,2\right]$ instead of assuming it always satisfies the classical finite variance assumption. To deal with this more challenging setting, people have proposed different algorithms and proved them to converge at an optimal $\mathcal{O}(T^{\frac{1-\mathfrak{p}}{3\mathfrak{p}-2}})$ rate for smooth objectives after $T$ iterations. Notably, all these new-designed algorithms are based on the same technique - gradient clipping. Naturally, one may want to know whether the clipping method is a necessary ingredient and the only way to guarantee convergence under heavy-tailed noises. In this work, by revisiting the existing Batched Normalized Stochastic Gradient Descent with Momentum (Batched NSGDM) algorithm, we provide the first convergence result under heavy-tailed noises but without gradient clipping. Concretely, we prove that Batched NSGDM can achieve the optimal $\mathcal{O}(T^{\frac{1-\mathfrak{p}}{3\mathfrak{p}-2}})$ rate even under the relaxed smooth condition. More interestingly, we also establish the first $\mathcal{O}(T^{\frac{1-\mathfrak{p}}{2\mathfrak{p}}})$ convergence rate in the case where the tail index $\mathfrak{p}$ is unknown in advance, which is arguably the common scenario in practice.

This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time and inferring changes later, we directly learn the differential parameter, i.e., the time derivative of the parameter. The main idea is treating the time score function of an exponential family model as a linear model of the differential parameter for direct estimation. We use time score matching to estimate parameter derivatives. We prove the consistency of a regularized score matching objective and demonstrate the finite-sample normality of a debiased estimator in high-dimensional settings. Our methodology effectively infers differential structures in high-dimensional graphical models, verified on simulated and real-world datasets.

Causal inference is a critical task across fields such as healthcare, economics, and the social sciences. While recent advances in machine learning, especially those based on the deep-learning architectures, have shown potential in estimating causal effects, existing approaches often fall short in handling complex causal structures and lack adaptability across various causal scenarios. In this paper, we present a novel transformer-based method for causal inference that overcomes these challenges. The core innovation of our model lies in its integration of causal Directed Acyclic Graphs (DAGs) directly into the attention mechanism, enabling it to accurately model the underlying causal structure. This allows for flexible estimation of both average treatment effects (ATE) and conditional average treatment effects (CATE). Extensive experiments on both synthetic and real-world datasets demonstrate that our approach surpasses existing methods in estimating causal effects across a wide range of scenarios. The flexibility and robustness of our model make it a valuable tool for researchers and practitioners tackling complex causal inference problems.

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously. We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system's hydraulic head responses.The conductivity field is represented with 706 degrees of freedom in the considered problem.The comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations' predictive posterior distribution at a fraction of the inference time of PEST-IES.

We study the problem of contextual dynamic pricing with a linear demand model. We propose a novel localized exploration-then-commit (LetC) algorithm which starts with a pure exploration stage, followed by a refinement stage that explores near the learned optimal pricing policy, and finally enters a pure exploitation stage. The algorithm is shown to achieve a minimax optimal, dimension-free regret bound when the time horizon exceeds a polynomial of the covariate dimension. Furthermore, we provide a general theoretical framework that encompasses the entire time spectrum, demonstrating how to balance exploration and exploitation when the horizon is limited. The analysis is powered by a novel critical inequality that depicts the exploration-exploitation trade-off in dynamic pricing, mirroring its existing counterpart for the bias-variance trade-off in regularized regression. Our theoretical results are validated by extensive experiments on synthetic and real-world data.

Pre-trained model assessment for transfer learning aims to identify the optimal candidate for the downstream tasks from a model hub, without the need of time-consuming fine-tuning. Existing advanced works mainly focus on analyzing the intrinsic characteristics of the entire features extracted by each pre-trained model or how well such features fit the target labels. This paper proposes a novel perspective for pre-trained model assessment through the Distribution of Spectral Components (DISCO). Through singular value decomposition of features extracted from pre-trained models, we investigate different spectral components and observe that they possess distinct transferability, contributing diversely to the fine-tuning performance. Inspired by this, we propose an assessment method based on the distribution of spectral components which measures the proportions of their corresponding singular values. Pre-trained models with features concentrating on more transferable components are regarded as better choices for transfer learning. We further leverage the labels of downstream data to better estimate the transferability of each spectral component and derive the final assessment criterion. Our proposed method is flexible and can be applied to both classification and regression tasks. We conducted comprehensive experiments across three benchmarks and two tasks including image classification and object detection, demonstrating that our method achieves state-of-the-art performance in choosing proper pre-trained models from the model hub for transfer learning.

The increasing scale of manycore systems poses significant challenges in managing reliability while meeting performance demands. Simultaneously, these systems become more susceptible to different aging mechanisms such as negative-bias temperature instability (NBTI), hot carrier injection (HCI), and thermal cycling (TC), as well as the electromigration (EM) phenomenon. In this paper, we propose a reinforcement learning (RL)-based task mapping method to improve the reliability of manycore systems considering the aforementioned aging mechanisms, which consists of three steps including bin packing, task-to-bin mapping, and task-to-core mapping. In the initial step, a density-based spatial application with noise (DBSCAN) clustering method is employed to compose some clusters (bins) based on the cores temperature. Then, the Q-learning algorithm is used for the two latter steps, to map the arrived task on a core such that the minimum thermal variation is occurred among all the bins. Compared to the state-of-the-art works, the proposed method is performed during runtime without requiring any parameter to be calculated offline. The effectiveness of the proposed technique is evaluated on 16, 32, and 64 cores systems using SPLASH2 and PARSEC benchmark suite applications. The results demonstrate up to 27% increase in the mean time to failure (MTTF) compared to the state-of-the-art task mapping techniques.

Visual Grounding aims to localize the referring object in an image given a natural language expression. Recent advancements in DETR-based visual grounding methods have attracted considerable attention, as they directly predict the coordinates of the target object without relying on additional efforts, such as pre-generated proposal candidates or pre-defined anchor boxes. However, existing research primarily focuses on designing stronger multi-modal decoder, which typically generates learnable queries by random initialization or by using linguistic embeddings. This vanilla query generation approach inevitably increases the learning difficulty for the model, as it does not involve any target-related information at the beginning of decoding. Furthermore, they only use the deepest image feature during the query learning process, overlooking the importance of features from other levels. To address these issues, we propose a novel approach, called RefFormer. It consists of the query adaption module that can be seamlessly integrated into CLIP and generate the referential query to provide the prior context for decoder, along with a task-specific decoder. By incorporating the referential query into the decoder, we can effectively mitigate the learning difficulty of the decoder, and accurately concentrate on the target object. Additionally, our proposed query adaption module can also act as an adapter, preserving the rich knowledge within CLIP without the need to tune the parameters of the backbone network. Extensive experiments demonstrate the effectiveness and efficiency of our proposed method, outperforming state-of-the-art approaches on five visual grounding benchmarks.