We derive and study time-uniform confidence spheres - termed confidence sphere sequences (CSSs) - which contain the mean of random vectors with high probability simultaneously across all sample sizes. Inspired by the original work of Catoni and Giulini, we unify and extend their analysis to cover both the sequential setting and to handle a variety of distributional assumptions. More concretely, our results include an empirical-Bernstein CSS for bounded random vectors (resulting in a novel empirical-Bernstein confidence interval), a CSS for sub-$\psi$ random vectors, and a CSS for heavy-tailed random vectors based on a sequentially valid Catoni-Giulini estimator. Finally, we provide a version of our empirical-Bernstein CSS that is robust to contamination by Huber noise.
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Generative Pre-trained Transformer (GPT) models have exhibited exciting progress in their capabilities, capturing the interest of practitioners and the public alike. Yet, while the literature on the trustworthiness of GPT models remains limited, practitioners have proposed employing capable GPT models for sensitive applications such as healthcare and finance -- where mistakes can be costly. To this end, this work proposes a comprehensive trustworthiness evaluation for large language models with a focus on GPT-4 and GPT-3.5, considering diverse perspectives -- including toxicity, stereotype bias, adversarial robustness, out-of-distribution robustness, robustness on adversarial demonstrations, privacy, machine ethics, and fairness. Based on our evaluations, we discover previously unpublished vulnerabilities to trustworthiness threats. For instance, we find that GPT models can be easily misled to generate toxic and biased outputs and leak private information in both training data and conversation history. We also find that although GPT-4 is usually more trustworthy than GPT-3.5 on standard benchmarks, GPT-4 is more vulnerable given jailbreaking system or user prompts, potentially because GPT-4 follows (misleading) instructions more precisely. Our work illustrates a comprehensive trustworthiness evaluation of GPT models and sheds light on the trustworthiness gaps. Our benchmark is publicly available at //decodingtrust.github.io/; our dataset can be previewed at //huggingface.co/datasets/AI-Secure/DecodingTrust; a concise version of this work is at //openreview.net/pdf?id=kaHpo8OZw2.
We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. Posterior samples are obtained by interpolating the predicted quantiles using monotonic cubic Hermite spline, with specific treatment for the tail behavior and multi-modal distributions. We introduce an alternative definition for the Bayesian credible region using the local Cumulative Density Function (CDF), offering substantially faster evaluation than the traditional Highest Posterior Density Region (HPDR). In case of limited simulation budget and/or known model misspecification, a post-processing broadening step can be integrated into NQE to ensure the unbiasedness of the posterior estimation with negligible additional computational cost. We demonstrate that the proposed NQE method achieves state-of-the-art performance on a variety of benchmark problems.
Semantic segmentation methods have advanced significantly. Still, their robustness to real-world perturbations and object types not seen during training remains a challenge, particularly in safety-critical applications. We propose a novel approach to improve the robustness of semantic segmentation techniques by leveraging the synergy between label-to-image generators and image-to-label segmentation models. Specifically, we design Robusta, a novel robust conditional generative adversarial network to generate realistic and plausible perturbed images that can be used to train reliable segmentation models. We conduct in-depth studies of the proposed generative model, assess the performance and robustness of the downstream segmentation network, and demonstrate that our approach can significantly enhance the robustness in the face of real-world perturbations, distribution shifts, and out-of-distribution samples. Our results suggest that this approach could be valuable in safety-critical applications, where the reliability of perception modules such as semantic segmentation is of utmost importance and comes with a limited computational budget in inference. We release our code at //github.com/ENSTA-U2IS/robusta.
Very recently, the first mathematical runtime analyses of the multi-objective evolutionary optimizer NSGA-II have been conducted. We continue this line of research with a first runtime analysis of this algorithm on a benchmark problem consisting of two multimodal objectives. We prove that if the population size $N$ is at least four times the size of the Pareto front, then the NSGA-II with four different ways to select parents and bit-wise mutation optimizes the OneJumpZeroJump benchmark with jump size~$2 \le k \le n/4$ in time $O(N n^k)$. When using fast mutation, a recently proposed heavy-tailed mutation operator, this guarantee improves by a factor of $k^{\Omega(k)}$. Overall, this work shows that the NSGA-II copes with the local optima of the OneJumpZeroJump problem at least as well as the global SEMO algorithm.
Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by planar triangles and careful design of numerical fluxes. The schemes are proven to be energy stable. Various numerical experiments are provided to validate the new schemes.
Background: Identifying and characterising the longitudinal patterns of multimorbidity associated with stroke is needed to better understand patients' needs and inform new models of care. Methods: We used an unsupervised patient-oriented clustering approach to analyse primary care electronic health records (EHR) of 30 common long-term conditions (LTC), in patients with stroke aged over 18, registered in 41 general practices in south London between 2005 and 2021. Results: Of 849,968 registered patients, 9,847 (1.16%) had a record of stroke, 46.5% were female and median age at record was 65.0 year (IQR: 51.5 to 77.0). The median number of LTCs in addition to stroke was 3 (IQR: from 2 to 5). Patients were stratified in eight clusters. These clusters revealed contrasted patterns of multimorbidity, socio-demographic characteristics (age, gender and ethnicity) and risk factors. Beside a core of 3 clusters associated with conventional stroke risk-factors, minor clusters exhibited less common but recurrent combinations of LTCs including mental health conditions, asthma, osteoarthritis and sickle cell anaemia. Importantly, complex profiles combining mental health conditions, infectious diseases and substance dependency emerged. Conclusion: This patient-oriented approach to EHRs uncovers the heterogeneity of profiles of multimorbidity and socio-demographic characteristics associated with stroke. It highlights the importance of conventional stroke risk factors as well as the association of mental health conditions in complex profiles of multimorbidity displayed in a significant proportion of patients. These results address the need for a better understanding of stroke-associated multimorbidity and complexity to inform more efficient and patient-oriented healthcare models.
We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless finite-state encoder that compresses the reconstruction codeword with no additional distortion. We first derive two different lower bounds to the compression ratio that depend on the number of states of the lossless encoder. Both bounds are asymptotically achievable by conceptually simple coding schemes. We then show that when the number of states of the lossless encoder is large enough in terms of the reconstruction block-length, the performance can be improved, sometimes significantly so. In particular, the improved performance is achievable using a random-coding ensemble that is universal, not only in terms of the source sequence, but also in terms of the distortion measure.
We address the choice of penalty parameter in the Smoothness-Penalized Deconvolution (SPeD) method of estimating a probability density under additive measurement error. Cross-validation gives an unbiased estimate of the risk (for the present sample size n) with a given penalty parameter, and this function can be minimized as a function of the penalty parameter. Least-squares cross-validation, which has been proposed for the similar Deconvoluting Kernel Density Estimator (DKDE), performs quite poorly for SPeD. We instead estimate the risk function for a smaller sample size n_1 < n with a given penalty parameter, using this to choose the penalty parameter for sample size n_1, and then use the asymptotics of the optimal penalty parameter to choose for sample size n. In a simulation study, we find that this has dramatically better performance than cross-validation, is an improvement over a SURE-type method previously proposed for this estimator, and compares favorably to the classic DKDE with its recommended plug-in method. We prove that the maximum error in estimating the risk function is of smaller order than its optimal rate of convergence.
Emotion recognition in conversation (ERC) aims to detect the emotion label for each utterance. Motivated by recent studies which have proven that feeding training examples in a meaningful order rather than considering them randomly can boost the performance of models, we propose an ERC-oriented hybrid curriculum learning framework. Our framework consists of two curricula: (1) conversation-level curriculum (CC); and (2) utterance-level curriculum (UC). In CC, we construct a difficulty measurer based on "emotion shift" frequency within a conversation, then the conversations are scheduled in an "easy to hard" schema according to the difficulty score returned by the difficulty measurer. For UC, it is implemented from an emotion-similarity perspective, which progressively strengthens the model's ability in identifying the confusing emotions. With the proposed model-agnostic hybrid curriculum learning strategy, we observe significant performance boosts over a wide range of existing ERC models and we are able to achieve new state-of-the-art results on four public ERC datasets.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
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