This paper examines the quantization methods used in large-scale data analysis models and their hyperparameter choices. The recent surge in data analysis scale has significantly increased computational resource requirements. To address this, quantizing model weights has become a prevalent practice in data analysis applications such as deep learning. Quantization is particularly vital for deploying large models on devices with limited computational resources. However, the selection of quantization hyperparameters, like the number of bits and value range for weight quantization, remains an underexplored area. In this study, we employ the typical case analysis from statistical physics, specifically the replica method, to explore the impact of hyperparameters on the quantization of simple learning models. Our analysis yields three key findings: (i) an unstable hyperparameter phase, known as replica symmetry breaking, occurs with a small number of bits and a large quantization width; (ii) there is an optimal quantization width that minimizes error; and (iii) quantization delays the onset of overparameterization, helping to mitigate overfitting as indicated by the double descent phenomenon. We also discover that non-uniform quantization can enhance stability. Additionally, we develop an approximate message-passing algorithm to validate our theoretical results.
相關內容
The objective of this paper is to provide an introduction to the principles of Bayesian joint modeling of longitudinal measurements and time-to-event outcomes, as well as model implementation using the BUGS language syntax. This syntax can be executed directly using OpenBUGS or by utilizing convenient functions to invoke OpenBUGS and JAGS from R software. In this paper, all details of joint models are provided, ranging from simple to more advanced models. The presentation started with the joint modeling of a Gaussian longitudinal marker and time-to-event outcome. The implementation of the Bayesian paradigm of the model is reviewed. The strategies for simulating data from the JM are also discussed. A proportional hazard model with various forms of baseline hazards, along with the discussion of all possible association structures between the two sub-models are taken into consideration. The paper covers joint models with multivariate longitudinal measurements, zero-inflated longitudinal measurements, competing risks, and time-to-event with cure fraction. The models are illustrated by the analyses of several real data sets. All simulated and real data and code are available at \url{//github.com/tbaghfalaki/JM-with-BUGS-and-JAGS}.
Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb R^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal O\!\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nystr\"om-based one) on $\mathbb R^d$.
Robotic manipulation relies on analytical or learned models to simulate the system dynamics. These models are often inaccurate and based on offline information, so that the robot planner is unable to cope with mismatches between the expected and the actual behavior of the system (e.g., the presence of an unexpected obstacle). In these situations, the robot should use information gathered online to correct its planning strategy and adapt to the actual system response. We propose a sampling-based motion planning approach that uses an estimate of the model error and online observations to correct the planning strategy at each new replanning. Our approach adapts the cost function and the sampling bias of a kinodynamic motion planner when the outcome of the executed transitions is different from the expected one (e.g., when the robot unexpectedly collides with an obstacle) so that future trajectories will avoid unreliable motions. To infer the properties of a new transition, we introduce the notion of context-awareness, i.e., we store local environment information for each executed transition and avoid new transitions with context similar to previous unreliable ones. This is helpful for leveraging online information even if the simulated transitions are far (in the state-and-action space) from the executed ones. Simulation and experimental results show that the proposed approach increases the success rate in execution and reduces the number of replannings needed to reach the goal.
This paper presents hybrid numerical techniques for solving the Boltzmann transport equation formulated by means of low-order equations for angular moments of the angular flux. The moment equations are derived by the projection operator approach. The projected equations are closed exactly using a high-order transport solution. The low-order equations of the hybrid methods are approximated with a finite volume scheme of the second-order accuracy. Functionals defining the closures in the discretized low-order equations are calculated by Monte Carlo techniques. In this study, we analyze effects of statistical noise and discretization error on the accuracy of the hybrid transport solution.
Synthetic data algorithms are widely employed in industries to generate artificial data for downstream learning tasks. While existing research primarily focuses on empirically evaluating utility of synthetic data, its theoretical understanding is largely lacking. This paper bridges the practice-theory gap by establishing relevant utility theory in a statistical learning framework. It considers two utility metrics: generalization and ranking of models trained on synthetic data. The former is defined as the generalization difference between models trained on synthetic and on real data. By deriving analytical bounds for this utility metric, we demonstrate that the synthetic feature distribution does not need to be similar as that of real data for ensuring comparable generalization of synthetic models, provided proper model specifications in downstream learning tasks. The latter utility metric studies the relative performance of models trained on synthetic data. In particular, we discover that the distribution of synthetic data is not necessarily similar as the real one to ensure consistent model comparison. Interestingly, consistent model comparison is still achievable even when synthetic responses are not well generated, as long as downstream models are separable by a generalization gap. Finally, extensive experiments on non-parametric models and deep neural networks have been conducted to validate these theoretical findings.
This paper considers the graph signal processing problem of anomaly detection in time series of graphs. We examine two related, complementary inference tasks: the detection of anomalous graphs within a time series, and the detection of temporally anomalous vertices. We approach these tasks via the adaptation of statistically principled methods for joint graph inference, specifically \emph{multiple adjacency spectral embedding} (MASE). We demonstrate that our method is effective for our inference tasks. Moreover, we assess the performance of our method in terms of the underlying nature of detectable anomalies. We further provide the theoretical justification for our method and insight into its use. Applied to the Enron communication graph and a large-scale commercial search engine time series of graphs, our approaches demonstrate their applicability and identify the anomalous vertices beyond just large degree change.
This paper contributes a formal framework for quantitative analysis of bounded sensor attacks on cyber-physical systems, using the formalism of differential dynamic logic. Given a precondition and postcondition of a system, we formalize two quantitative safety notions, quantitative forward and backward safety, which respectively express (1) how strong the strongest postcondition of the system is with respect to the specified postcondition, and (2) how strong the specified precondition is with respect to the weakest precondition of the system needed to ensure the specified postcondition holds. We introduce two notions, forward and backward robustness, to characterize the robustness of a system against sensor attacks as the loss of safety. To reason about robustness, we introduce two simulation distances, forward and backward simulation distances, which are defined based on the behavioral distances between the original system and the system with compromised sensors. Forward and backward distances, respectively, characterize upper bounds of the degree of forward and backward safety loss caused by the sensor attacks. We verify the two simulation distances by expressing them as modalities, i.e., formulas of differential dynamic logic, and develop an ad-hoc proof system to reason with such formulas. We showcase our formal notions and reasoning techniques on two non-trivial case studies: an autonomous vehicle that needs to avoid collision and a water tank system.
In general, diffusion model-based MRI reconstruction methods incrementally remove artificially added noise while imposing data consistency to reconstruct the underlying images. However, real-world MRI acquisitions already contain inherent noise due to thermal fluctuations. This phenomenon is particularly notable when using ultra-fast, high-resolution imaging sequences for advanced research, or using low-field systems favored by low- and middle-income countries. These common scenarios can lead to sub-optimal performance or complete failure of existing diffusion model-based reconstruction techniques. Specifically, as the artificially added noise is gradually removed, the inherent MRI noise becomes increasingly pronounced, making the actual noise level inconsistent with the predefined denoising schedule and consequently inaccurate image reconstruction. To tackle this problem, we propose a posterior sampling strategy with a novel NoIse Level Adaptive Data Consistency (Nila-DC) operation. Extensive experiments are conducted on two public datasets and an in-house clinical dataset with field strength ranging from 0.3T to 3T, showing that our method surpasses the state-of-the-art MRI reconstruction methods, and is highly robust against various noise levels. The code will be released after review.
In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.
We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, called the judge, decides whether the fact is true or false. The two agents can be considered as sparse, adversarial feature generators that present interpretable evidence for either the thesis or the antithesis. In contrast to other black-box methods, the arguments allow users to get an understanding of the decision of the judge. Since the focus of this work is to create an explainable method that maintains a competitive predictive accuracy, we benchmark our method on the triple classification and link prediction task. Thereby, we find that our method outperforms several baselines on the benchmark datasets FB15k-237, WN18RR, and Hetionet. We also conduct a survey and find that the extracted arguments are informative for users.
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