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In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate the quantification of uncertainty in the parameter identification process. A significant challenge in this context is the numerical integration of continuous-time ordinary differential equations (ODEs), crucial for aligning theoretical models with discretely sampled data. This integration introduces additional numerical uncertainty, a factor that is often over looked. To address this issue, the field of probabilistic numerics combines numerical methods, such as numerical integration, with probabilistic modeling to offer a more comprehensive analysis of total uncertainty. By retaining the accuracy of classical deterministic methods, these probabilistic approaches offer a deeper understanding of the uncertainty inherent in the inference process. This paper demonstrates the application of a probabilistic numerical method for solving ODEs in the joint parameter-state identification of nonlinear dynamic systems. The presented approach efficiently identifies latent states and system parameters from noisy measurements. Simultaneously incorporating probabilistic solutions to the ODE in the identification challenge. The methodology's primary advantage lies in its capability to produce posterior distributions over system parameters, thereby representing the inherent uncertainties in both the data and the identification process.

The ability of the foundation models heavily relies on large-scale, diverse, and high-quality pretraining data. In order to improve data quality, researchers and practitioners often have to manually curate datasets from difference sources and develop dedicated data cleansing pipeline for each data repository. Lacking a unified data processing framework, this process is repetitive and cumbersome. To mitigate this issue, we propose a data processing framework that integrates a Processing Module which consists of a series of operators at different granularity levels, and an Analyzing Module which supports probing and evaluation of the refined data. The proposed framework is easy to use and highly flexible. In this demo paper, we first introduce how to use this framework with some example use cases and then demonstrate its effectiveness in improving the data quality with an automated evaluation with ChatGPT and an end-to-end evaluation in pretraining the GPT-2 model. The code and demonstration videos are accessible on GitHub.

Imputation methods for dealing with incomplete data typically assume that the missingness mechanism is at random (MAR). These methods can also be applied to missing not at random (MNAR) situations, where the user specifies some adjustment parameters that describe the degree of departure from MAR. The effect of different pre-chosen values is then studied on the inferences. This paper proposes a novel imputation method, the Random Indicator (RI) method, which, in contrast to the current methodology, estimates these adjustment parameters from the data. For an incomplete variable $X$, the RI method assumes that the observed part of $X$ is normal and the probability for $X$ to be missing follows a logistic function. The idea is to estimate the adjustment parameters by generating a pseudo response indicator from this logistic function. Our method iteratively draws imputations for $X$ and the realization of the response indicator $R$, to which we refer as $\dot{R}$, for $X$. By cross-classifying $X$ by $R$ and $\dot{R}$, we obtain various properties on the distribution of the missing data. These properties form the basis for estimating the degree of departure from MAR. Our numerical simulations show that the RI method performs very well across a variety of situations. We show how the method can be used in a real life data set. The RI method is automatic and opens up new ways to tackle the problem of MNAR data.

Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator Hamiltonians. Ordinarily, these data-encoding generators are chosen in advance, fixing the space of functions that can be represented. In this work we consider a generalization of quantum models to include a set of trainable parameters in the generator, leading to a trainable frequency (TF) quantum model. We numerically demonstrate how TF models can learn generators with desirable properties for solving the task at hand, including non-regularly spaced frequencies in their spectra and flexible spectral richness. Finally, we showcase the real-world effectiveness of our approach, demonstrating an improved accuracy in solving the Navier-Stokes equations using a TF model with only a single parameter added to each encoding operation. Since TF models encompass conventional fixed frequency models, they may offer a sensible default choice for variational quantum machine learning.

Explainability is a key component in many applications involving deep neural networks (DNNs). However, current explanation methods for DNNs commonly leave it to the human observer to distinguish relevant explanations from spurious noise. This is not feasible anymore when going from easily human-accessible data such as images to more complex data such as genome sequences. To facilitate the accessibility of DNN outputs from such complex data and to increase explainability, we present a modification of the widely used explanation method layer-wise relevance propagation. Our approach enforces sparsity directly by pruning the relevance propagation for the different layers. Thereby, we achieve sparser relevance attributions for the input features as well as for the intermediate layers. As the relevance propagation is input-specific, we aim to prune the relevance propagation rather than the underlying model architecture. This allows to prune different neurons for different inputs and hence, might be more appropriate to the local nature of explanation methods. To demonstrate the efficacy of our method, we evaluate it on two types of data, images and genomic sequences. We show that our modification indeed leads to noise reduction and concentrates relevance on the most important features compared to the baseline.

Accurate uncertainty estimates are important in sequential model-based decision-making tasks such as Bayesian optimization. However, these estimates can be imperfect if the data violates assumptions made by the model (e.g., Gaussianity). This paper studies which uncertainties are needed in model-based decision-making and in Bayesian optimization, and argues that uncertainties can benefit from calibration -- i.e., an 80% predictive interval should contain the true outcome 80% of the time. Maintaining calibration, however, can be challenging when the data is non-stationary and depends on our actions. We propose using simple algorithms based on online learning to provably maintain calibration on non-i.i.d. data, and we show how to integrate these algorithms in Bayesian optimization with minimal overhead. Empirically, we find that calibrated Bayesian optimization converges to better optima in fewer steps, and we demonstrate improved performance on standard benchmark functions and hyperparameter optimization tasks.

Transaction fee mechanism design is a new decentralized mechanism design problem where users bid for space on the blockchain. Several recent works showed that the transaction fee mechanism design fundamentally departs from classical mechanism design. They then systematically explored the mathematical landscape of this new decentralized mechanism design problem in two settings: in the plain setting where no cryptography is employed, and in a cryptography-assisted setting where the rules of the mechanism are enforced by a multi-party computation protocol. Unfortunately, in both settings, prior works showed that if we want the mechanism to incentivize honest behavior for both users as well as miners (possibly colluding with users), then the miner revenue has to be zero. Although adopting a relaxed, approximate notion of incentive compatibility gets around this zero miner-revenue limitation, the scaling of the miner revenue is nonetheless poor. In this paper, we show that if we make a mildly stronger reasonable-world assumption than prior works, we can circumvent the known limitations on miner revenue, and design auctions that generate optimal miner revenue. We also systematically explore the mathematical landscape of transaction fee mechanism design under the new reasonable-world and demonstrate how such assumptions can alter the feasibility and infeasibility landscape.

Stream processing is usually done either on a tuple-by-tuple basis or in micro-batches. There are many applications where tuples over a predefined duration/window must be processed within certain deadlines. Processing such queries using stream processing engines can be very inefficient since there is often a significant overhead per tuple or micro-batch. The cost of computation can be significantly reduced by using the wider window available for computation. In this work, we present scheduling schemes where the overhead cost is minimized while meeting the query deadline constraints. For such queries, since the result is needed only at the deadline, tuples can be processed in larger batches, instead of using micro-batches. We present scheduling schemes for single and multi query scenarios. The proposed scheduling algorithms have been implemented as a Custom Query Scheduler, on top of Apache Spark. Our performance study with TPC-H data, under single and multi query modes, shows orders of magnitude improvement as compared to naively using Spark streaming.

With the flourishing development of intelligent warehousing systems, the technology of Automated Guided Vehicle (AGV) has experienced rapid growth. Within intelligent warehousing environments, AGV is required to safely and rapidly plan an optimal path in complex and dynamic environments. Most research has studied deep reinforcement learning to address this challenge. However, in the environments with sparse extrinsic rewards, these algorithms often converge slowly, learn inefficiently or fail to reach the target. Random Network Distillation (RND), as an exploration enhancement, can effectively improve the performance of proximal policy optimization, especially enhancing the additional intrinsic rewards of the AGV agent which is in sparse reward environments. Moreover, most of the current research continues to use 2D grid mazes as experimental environments. These environments have insufficient complexity and limited action sets. To solve this limitation, we present simulation environments of AGV path planning with continuous actions and positions for AGVs, so that it can be close to realistic physical scenarios. Based on our experiments and comprehensive analysis of the proposed method, the results demonstrate that our proposed method enables AGV to more rapidly complete path planning tasks with continuous actions in our environments. A video of part of our experiments can be found at //youtu.be/lwrY9YesGmw.

This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.