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.

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.

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.

We study reinforcement learning (RL) for decision processes with non-Markovian reward, in which high-level knowledge of the task in the form of reward machines is available to the learner. We consider probabilistic reward machines with initially unknown dynamics, and investigate RL under the average-reward criterion, where the learning performance is assessed through the notion of regret. Our main algorithmic contribution is a model-based RL algorithm for decision processes involving probabilistic reward machines that is capable of exploiting the structure induced by such machines. We further derive high-probability and non-asymptotic bounds on its regret and demonstrate the gain in terms of regret over existing algorithms that could be applied, but obliviously to the structure. We also present a regret lower bound for the studied setting. To the best of our knowledge, the proposed algorithm constitutes the first attempt to tailor and analyze regret specifically for RL with probabilistic reward machines.

Real-time bidding (RTB) plays a pivotal role in online advertising ecosystems. Advertisers employ strategic bidding to optimize their advertising impact while adhering to various financial constraints, such as the return-on-investment (ROI) and cost-per-click (CPC). Primarily focusing on bidding with fixed budget constraints, traditional approaches cannot effectively manage the dynamic budget allocation problem where the goal is to achieve global optimization of bidding performance across multiple channels with a shared budget. In this paper, we propose a hierarchical multi-agent reinforcement learning framework for multi-channel bidding optimization. In this framework, the top-level strategy applies a CPC constrained diffusion model to dynamically allocate budgets among the channels according to their distinct features and complex interdependencies, while the bottom-level strategy adopts a state-action decoupled actor-critic method to address the problem of extrapolation errors in offline learning caused by out-of-distribution actions and a context-based meta-channel knowledge learning method to improve the state representation capability of the policy based on the shared knowledge among different channels. Comprehensive experiments conducted on a large scale real-world industrial dataset from the Meituan ad bidding platform demonstrate that our method achieves a state-of-the-art performance.

We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common distribution with an unknown parameter (vector). This parameter belongs to either a normal or abnormal space depending on the current state of the process. Before the change point, all processes, including the anomalous one, are in a normal state; after the change point, the anomalous process transitions to an abnormal state. Our goal is to design a sequential search strategy that minimizes the Bayes risk by balancing sample complexity and detection accuracy. We propose a deterministic search algorithm with the following notable properties. First, we analytically demonstrate that when the distributions of both normal and abnormal processes are unknown, the algorithm is asymptotically optimal in minimizing the Bayes risk as the error probability approaches zero. In the second setting, where the parameter under the null hypothesis is known, the algorithm achieves asymptotic optimality with improved detection time based on the true normal state. Simulation results are presented to validate the theoretical findings.

The proliferation of malware variants poses a significant challenges to traditional malware detection approaches, such as signature-based methods, necessitating the development of advanced machine learning techniques. In this research, we present a novel approach based on a hybrid architecture combining features extracted using a Hidden Markov Model (HMM), with a Convolutional Neural Network (CNN) then used for malware classification. Inspired by the strong results in previous work using an HMM-Random Forest model, we propose integrating HMMs, which serve to capture sequential patterns in opcode sequences, with CNNs, which are adept at extracting hierarchical features. We demonstrate the effectiveness of our approach on the popular Malicia dataset, and we obtain superior performance, as compared to other machine learning methods -- our results surpass the aforementioned HMM-Random Forest model. Our findings underscore the potential of hybrid HMM-CNN architectures in bolstering malware classification capabilities, offering several promising avenues for further research in the field of cybersecurity.

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have proposed such decompositions, they lack the type of formal guarantees we provide. Our method is based on the new notion of higher-order calibration, which generalizes ordinary calibration to the setting of higher-order predictors that predict mixtures over label distributions at every point. We show how to measure as well as achieve higher-order calibration using access to $k$-snapshots, namely examples where each point has $k$ independent conditional labels. Under higher-order calibration, the estimated aleatoric uncertainty at a point is guaranteed to match the real-world aleatoric uncertainty averaged over all points where the prediction is made. To our knowledge, this is the first formal guarantee of this type that places no assumptions whatsoever on the real-world data distribution. Importantly, higher-order calibration is also applicable to existing higher-order predictors such as Bayesian and ensemble models and provides a natural evaluation metric for such models. We demonstrate through experiments that our method produces meaningful uncertainty decompositions for image classification.

Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov Chain Monte Carlo methods face slow convergence and computational burdens. Existing Variational Inference methods, which require pre-generated topologies and typically treat tree structures and branch lengths independently, may overlook critical sequence features, limiting their accuracy and flexibility. We propose PhyloGen, a novel method leveraging a pre-trained genomic language model to generate and optimize phylogenetic trees without dependence on evolutionary models or aligned sequence constraints. PhyloGen views phylogenetic inference as a conditionally constrained tree structure generation problem, jointly optimizing tree topology and branch lengths through three core modules: (i) Feature Extraction, (ii) PhyloTree Construction, and (iii) PhyloTree Structure Modeling. Meanwhile, we introduce a Scoring Function to guide the model towards a more stable gradient descent. We demonstrate the effectiveness and robustness of PhyloGen on eight real-world benchmark datasets. Visualization results confirm PhyloGen provides deeper insights into phylogenetic relationships.

Adaptive Traffic Signal Control (ATSC) system is a critical component of intelligent transportation, with the capability to significantly alleviate urban traffic congestion. Although reinforcement learning (RL)-based methods have demonstrated promising performance in achieving ATSC, existing methods are still prone to making unreasonable policies. Therefore, this paper proposes a novel Bayesian Critique-Tune-Based Reinforcement Learning with Adaptive Pressure for multi-intersection signal control (BCT-APLight). In BCT-APLight, the Critique-Tune (CT) framework, a two-layer Bayesian structure is designed to refine the excessive trust of RL policies. Specifically, the Bayesian inference-based Critique Layer provides effective evaluations of the credibility of policies; the Bayesian decision-based Tune Layer fine-tunes policies by minimizing the posterior risks when the evaluations are negative. Meanwhile, an attention-based Adaptive Pressure (AP) mechanism is designed to effectively weight the vehicle queues in each lane, thereby enhancing the rationality of traffic movement representation within the network. Equipped with the CT framework and AP mechanism, BCT-APLight effectively enhances the reasonableness of RL policies. Extensive experiments conducted with a simulator across a range of intersection layouts demonstrate that BCT-APLight is superior to other state-of-the-art (SOTA) methods on seven real-world datasets. Specifically, BCT-APLight decreases average queue length by \textbf{\(\boldsymbol{9.60\%}\)} and average waiting time by \textbf{\(\boldsymbol{15.28\%}\)}.