We propose a new measure of systemic risk to analyze the impact of the major financial market turmoils in the stock markets from 2000 to 2023 in the USA, Europe, Brazil, and Japan. Our Implied Volatility Realized Volatility Systemic Risk Indicator (IVRVSRI) shows that the reaction of stock markets varies across different geographical locations and the persistence of the shocks depends on the historical volatility and long-term average volatility level in a given market. The methodology applied is based on the logic that the simpler is always better than the more complex if it leads to the same results. Such an approach significantly limits model risk and substantially decreases computational burden. Robustness checks show that IVRVSRI is a precise and valid measure of the current systemic risk in the stock markets. Moreover, it can be used for other types of assets and high-frequency data. The forecasting ability of various SRIs (including CATFIN, CISS, IVRVSRI, SRISK, and Cleveland FED) with regard to weekly returns of S&P 500 index is evaluated based on the simple linear, quasi-quantile, and quantile regressions. We show that IVRVSRI has the strongest predicting power among them.
As machine learning gains prominence in various sectors of society for automated decision-making, concerns have risen regarding potential vulnerabilities in machine learning (ML) frameworks. Nevertheless, testing these frameworks is a daunting task due to their intricate implementation. Previous research on fuzzing ML frameworks has struggled to effectively extract input constraints and generate valid inputs, leading to extended fuzzing durations for deep execution or revealing the target crash. In this paper, we propose ConFL, a constraint-guided fuzzer for ML frameworks. ConFL automatically extracting constraints from kernel codes without the need for any prior knowledge. Guided by the constraints, ConFL is able to generate valid inputs that can pass the verification and explore deeper paths of kernel codes. In addition, we design a grouping technique to boost the fuzzing efficiency. To demonstrate the effectiveness of ConFL, we evaluated its performance mainly on Tensorflow. We find that ConFL is able to cover more code lines, and generate more valid inputs than state-of-the-art (SOTA) fuzzers. More importantly, ConFL found 84 previously unknown vulnerabilities in different versions of Tensorflow, all of which were assigned with new CVE ids, of which 3 were critical-severity and 13 were high-severity. We also extended ConFL to test PyTorch and Paddle, 7 vulnerabilities are found to date.
We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically and computationally) is investigated and two algorithms based on Gibbs sampling and Stochastic Localization are analyzed, both under the same (quite natural) statistical assumptions that also enable valid inference on the sparse planted signal. The benefit of the Stochastic Localization sampler is particularly prominent for data matrix that is not well-designed.
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain quantitative bounds on normal approximations valid at large but finite $n$ and any fixed network depth. Our theorems show both for the finite-dimensional distributions and the entire process, that the distance between a random fully connected network (and its derivatives) to the corresponding infinite width Gaussian process scales like $n^{-\gamma}$ for $\gamma>0$, with the exponent depending on the metric used to measure discrepancy. Our bounds are strictly stronger in terms of their dependence on network width than any previously available in the literature; in the one-dimensional case, we also prove that they are optimal, i.e., we establish matching lower bounds.
In previous work ("Knowledge from Probability", TARK 2021) we develop a question-relative, probabilistic account of belief. On this account, what someone believes relative to a given question is (i) closed under entailment, (ii) sufficiently probable given their evidence, and (iii) sensitive to the relative probabilities of the answers to the question. Here we explore the implications of this account for the dynamics of belief. We show that the principles it validates are much weaker than those of orthodox theories of belief revision like AGM, but still stronger than those valid according to the popular Lockean theory of belief, which equates belief with high subjective probability. We then consider a restricted class of models, suitable for many but not all applications, and identify some further natural principles valid on this class. We conclude by arguing that the present framework compares favorably to the rival probabilistic accounts of belief developed by Leitgeb and by Lin and Kelly.
Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural sciences. While many of these problems stand to benefit from the ability to specify arbitrary, domain-informed constraints, this setting is not covered by the existing (Riemannian) diffusion model methodology. Recent work has attempted to address this issue by constructing novel noising processes based on the reflected Brownian motion and logarithmic barrier methods. However, the associated samplers are either computationally burdensome or only apply to convex subsets of Euclidean space. In this paper, we introduce an alternative, simple noising scheme based on Metropolis sampling that affords substantial gains in computational efficiency and empirical performance compared to the earlier samplers. Of independent interest, we prove that this new process corresponds to a valid discretisation of the reflected Brownian motion. We demonstrate the scalability and flexibility of our approach on a range of problem settings with convex and non-convex constraints, including applications from geospatial modelling, robotics and protein design.
Given a sequence of observable variables $\{(x_1, y_1), \ldots, (x_n, y_n)\}$, the conformal prediction method estimates a confidence set for $y_{n+1}$ given $x_{n+1}$ that is valid for any finite sample size by merely assuming that the joint distribution of the data is permutation invariant. Although attractive, computing such a set is computationally infeasible in most regression problems. Indeed, in these cases, the unknown variable $y_{n+1}$ can take an infinite number of possible candidate values, and generating conformal sets requires retraining a predictive model for each candidate. In this paper, we focus on a sparse linear model with only a subset of variables for prediction and use numerical continuation techniques to approximate the solution path efficiently. The critical property we exploit is that the set of selected variables is invariant under a small perturbation of the input data. Therefore, it is sufficient to enumerate and refit the model only at the change points of the set of active features and smoothly interpolate the rest of the solution via a Predictor-Corrector mechanism. We show how our path-following algorithm accurately approximates conformal prediction sets and illustrate its performance using synthetic and real data examples.
In open-domain question answering, due to the ambiguity of questions, multiple plausible answers may exist. To provide feasible answers to an ambiguous question, one approach is to directly predict all valid answers, but this can struggle with balancing relevance and diversity. An alternative is to gather candidate answers and aggregate them, but this method can be computationally costly and may neglect dependencies among answers. In this paper, we present AmbigPrompt to address the imperfections of existing approaches to answering ambiguous questions. Specifically, we integrate an answering model with a prompting model in an iterative manner. The prompting model adaptively tracks the reading process and progressively triggers the answering model to compose distinct and relevant answers. Additionally, we develop a task-specific post-pretraining approach for both the answering model and the prompting model, which greatly improves the performance of our framework. Empirical studies on two commonly-used open benchmarks show that AmbigPrompt achieves state-of-the-art or competitive results while using less memory and having a lower inference latency than competing approaches. Additionally, AmbigPrompt also performs well in low-resource settings. The code are available at: https://github.com/sunnweiwei/AmbigPrompt.
This paper presents an automated algorithm to analyze the stability of piecewise affine (PWA) dynamical systems due to their broad applications. We parametrize the Lyapunov function as a PWA function, with polytopic regions defined by the PWA dynamics. Using this parametrization, Stability conditions can be expressed as linear constraints restricted to polytopes so that the search for a Lyapunov function involves solving a linear program. However, a valid Lyapunov function might not be found given these polytopic regions. A natural response is to increase the size of the parametrization of the Lyapunov function by dividing regions and solving the new linear program. This paper proposes two new methods to divide each polytope into smaller ones. The first approach divides a polytope based on the sign of the derivative of the candidate Lyapunov function, while the second divides it based on the change in the vector field of the PWA dynamical system. In addition, we propose using Delaunay triangulation to achieve automated division of regions and preserve the continuity of the PWA Lyapunov function. Examples involving learned models and explicit MPC controllers demonstrate that the proposed method of dividing regions leads to valid Lyapunov functions with fewer regions than existing methods, reducing the computational time taken for stability analysis
Despite the impressive prediction ability, machine learning models show discrimination towards certain demographics and suffer from unfair prediction behaviors. To alleviate the discrimination, extensive studies focus on eliminating the unequal distribution of sensitive attributes via multiple approaches. However, due to privacy concerns, sensitive attributes are often either unavailable or missing in real-world scenarios. Therefore, several existing works alleviate the bias without sensitive attributes. Those studies face challenges, either in inaccurate predictions of sensitive attributes or the need to mitigate unequal distribution of manually defined non-sensitive attributes related to bias. The latter requires strong assumptions about the correlation between sensitive and non-sensitive attributes. As data distribution and task goals vary, the strong assumption on non-sensitive attributes may not be valid and require domain expertise. In this work, we propose an assumption-free framework to detect the related attributes automatically by modeling feature interaction for bias mitigation. The proposed framework aims to mitigate the unfair impact of identified biased feature interactions. Experimental results on four real-world datasets demonstrate that our proposed framework can significantly alleviate unfair prediction behaviors by considering biased feature interactions.
This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We establish a proper theoretical characterization of this problem via a two-step procedure. First, we examine the asymptotic terminal behavior of the value function, which implies that any transaction close to maturity only provides a marginal contribution to the utility. Second, we establish the theoretical foundation in terms of the discontinuous viscosity solution, incorporating the proper characterization of the terminal condition. Via extensive numerical analyses involving several types of utility functions, we find that the introduction of transaction costs into non-concave utility maximization problems can make it optimal for investors to hold on to a larger long position in the risky asset compared to the frictionless case, or hold on to a large short position in the risky asset despite a positive risk premium.
Large documents written in juridical language are difficult to interpret, with long sentences leading to intricate and intertwined relations between the nouns. The present paper frames this problem in the context of recent European security directives. The complexity of their language is here thwarted by automating the extraction of the relevant information, namely of the parts of speech from each clause, through a specific tailoring of Natural Language Processing (NLP) techniques. These contribute, in combination with ontology development principles, to the design of our automated method for the representation of security directives as ontologies. The method is showcased on a practical problem, namely to derive an ontology representing the NIS 2 directive, which is the peak of cybersecurity prescripts at the European level. Although the NLP techniques adopted showed some limitations and had to be complemented by manual analysis, the overall results provide valid support for directive compliance in general and for ontology development in particular.
Cross-validation is a widely used technique for evaluating the performance of prediction models. It helps avoid the optimism bias in error estimates, which can be significant for models built using complex statistical learning algorithms. However, since the cross-validation estimate is a random value dependent on observed data, it is essential to accurately quantify the uncertainty associated with the estimate. This is especially important when comparing the performance of two models using cross-validation, as one must determine whether differences in error estimates are a result of chance fluctuations. Although various methods have been developed for making inferences on cross-validation estimates, they often have many limitations, such as stringent model assumptions This paper proposes a fast bootstrap method that quickly estimates the standard error of the cross-validation estimate and produces valid confidence intervals for a population parameter measuring average model performance. Our method overcomes the computational challenge inherent in bootstrapping the cross-validation estimate by estimating the variance component within a random effects model. It is just as flexible as the cross-validation procedure itself. To showcase the effectiveness of our approach, we employ comprehensive simulations and real data analysis across three diverse applications.
The development of plans of action in disaster response scenarios is a time-consuming process. Large Language Models (LLMs) offer a powerful solution to expedite this process through in-context learning. This study presents DisasterResponseGPT, an algorithm that leverages LLMs to generate valid plans of action quickly by incorporating disaster response and planning guidelines in the initial prompt. In DisasterResponseGPT, users input the scenario description and receive a plan of action as output. The proposed method generates multiple plans within seconds, which can be further refined following the user's feedback. Preliminary results indicate that the plans of action developed by DisasterResponseGPT are comparable to human-generated ones while offering greater ease of modification in real-time. This approach has the potential to revolutionize disaster response operations by enabling rapid updates and adjustments during the plan's execution.
The advent of large language models (LLMs) has revolutionized natural language processing, enabling the generation of coherent and contextually relevant human-like text. As LLMs increasingly powerconversational agents used by the general public world-wide, the synthetic personality traits embedded in these models, by virtue of training on large amounts of human data, is becoming increasingly important. Since personality is a key factor determining the effectiveness of communication, we present a novel and comprehensive psychometrically valid and reliable methodology for administering and validating personality tests on widely-used LLMs, as well as for shaping personality in the generated text of such LLMs. Applying this method to 18 LLMs, we found: 1) personality measurements in the outputs of some LLMs under specific prompting configurations are reliable and valid; 2) evidence of reliability and validity of synthetic LLM personality is stronger for larger and instruction fine-tuned models; and 3) personality in LLM outputs can be shaped along desired dimensions to mimic specific human personality profiles. We discuss the application and ethical implications of the measurement and shaping method, in particular regarding responsible AI.
Research into 6G networks has been initiated to support a variety of critical artificial intelligence (AI) assisted applications such as autonomous driving. In such applications, AI-based decisions should be performed in a real-time manner. These decisions include resource allocation, localization, channel estimation, etc. Considering the black-box nature of existing AI-based models, it is highly challenging to understand and trust the decision-making behavior of such models. Therefore, explaining the logic behind those models through explainable AI (XAI) techniques is essential for their employment in critical applications. This manuscript proposes a novel XAI-based channel estimation (XAI-CHEST) scheme that provides detailed reasonable interpretability of the deep learning (DL) models that are employed in doubly-selective channel estimation. The aim of the proposed XAI-CHEST scheme is to identify the relevant model inputs by inducing high noise on the irrelevant ones. As a result, the behavior of the studied DL-based channel estimators can be further analyzed and evaluated based on the generated interpretations. Simulation results show that the proposed XAI-CHEST scheme provides valid interpretations of the DL-based channel estimators for different scenarios.
Deep Neural Networks have achieved great success in some of the complex tasks that humans can do with ease. These include image recognition/classification, natural language processing, game playing etc. However, modern Neural Networks fail or perform poorly when trained on tasks that can be solved easily using backtracking and traditional algorithms. Therefore, we use the architecture of the Neuro Logic Machine (NLM) and extend its functionality to solve a 9X9 game of Sudoku. To expand the application of NLMs, we generate a random grid of cells from a dataset of solved games and assign up to 10 new empty cells. The goal of the game is then to find a target value ranging from 1 to 9 and fill in the remaining empty cells while maintaining a valid configuration. In our study, we showcase an NLM which is capable of obtaining 100% accuracy for solving a Sudoku with empty cells ranging from 3 to 10. The purpose of this study is to demonstrate that NLMs can also be used for solving complex problems and games like Sudoku. We also analyze the behaviour of NLMs with a backtracking algorithm by comparing the convergence time using a graph plot on the same problem. With this study we show that Neural Logic Machines can be trained on the tasks that traditional Deep Learning architectures fail using Reinforcement Learning. We also aim to propose the importance of symbolic learning in explaining the systematicity in the hybrid model of NLMs.
Virtual acoustic environments enable the creation and simulation of realistic and ecologically valid daily-life situations with applications in hearing research and audiology. Hereby, reverberant indoor environments play an important role. For real-time applications, simplifications in the room acoustics simulation are required, however, it remains unclear what acoustic level of detail (ALOD) is necessary to capture all perceptually relevant effects. This study investigates the effect of varying ALOD in the simulation of three different real environments, a living room with a coupled kitchen, a pub, and an underground station. ALOD was varied by generating different numbers of image sources for early reflections, or by excluding geometrical room details specific for each environment. The simulations were perceptually evaluated using headphones in comparison to binaural room impulse responses measured with a dummy head in the corresponding real environments, and partly using loudspeakers. The study assessed the perceived overall difference for a pulse, and a speech token. Furthermore, plausibility and externalization were evaluated. The results show that a strong reduction in ALOD is possible while obtaining similar plausibility and externalization as with the dummy head recordings. The number and accuracy of early reflections appear less relevant, provided diffuse late reverberation is appropriately accounted for.
We investigate a version of linear temporal logic whose propositional fragment is G\"odel-Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics: first a real-valued semantics, where statements have a degree of truth in the real unit interval and second a `bi-relational' semantics. We then show that these two semantics indeed define one and the same logic: the statements that are valid for the real-valued semantics are the same as those that are valid for the bi-relational semantics. This G\"odel temporal logic does not have any form of the finite model property for these two semantics: there are non-valid statements that can only be falsified on an infinite model. However, by using the technical notion of a quasimodel, we show that every falsifiable statement is falsifiable on a finite quasimodel, yielding an algorithm for deciding if a statement is valid or not. Later, we strengthen this decidability result by giving an algorithm that uses only a polynomial amount of memory, proving that G\"odel temporal logic is PSPACE-complete. We also provide a deductive calculus for G\"odel temporal logic, and show this calculus to be sound and complete for the above-mentioned semantics, so that all (and only) the valid statements can be proved with this calculus.
Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically intractable. We present an algorithm for simulating values from a counterfactual distribution where conditions can be set on both discrete and continuous variables. We show that the proposed algorithm can be presented as a particle filter leading to asymptotically valid inference. The algorithm is applied to fairness analysis in credit-scoring.