亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Differentially private mechanisms achieving worst-case optimal error bounds (e.g., the classical Laplace mechanism) are well-studied in the literature. However, when typical data are far from the worst case, \emph{instance-specific} error bounds -- which depend on the largest value in the dataset -- are more meaningful. For example, consider the sum estimation problem, where each user has an integer $x_i$ from the domain $\{0,1,\dots,U\}$ and we wish to estimate $\sum_i x_i$. This has a worst-case optimal error of $O(U/\varepsilon)$, while recent work has shown that the clipping mechanism can achieve an instance-optimal error of $O(\max_i x_i \cdot \log\log U /\varepsilon)$. Under the shuffle model, known instance-optimal protocols are less communication-efficient. The clipping mechanism also works in the shuffle model, but requires two rounds: Round one finds the clipping threshold, and round two does the clipping and computes the noisy sum of the clipped data. In this paper, we show how these two seemingly sequential steps can be done simultaneously in one round using just $1+o(1)$ messages per user, while maintaining the instance-optimal error bound. We also extend our technique to the high-dimensional sum estimation problem and sparse vector aggregation (a.k.a. frequency estimation under user-level differential privacy). Our experiments show order-of-magnitude improvements of our protocols in terms of error compared with prior work.

Dislocations are the primary carriers of plasticity in metallic material. Understanding the basic mechanisms for dislocation movement is paramount to predicting the material mechanical response. Relying on atomistic simulations, we observe a transition from non-Arrhenius to Arrhenius behavior in the rate for an edge dislocation to overcome the elastic interaction with a prismatic loop in tungsten. Beyond the critical resolved shear stress, the process shows a non-Arrhenius behavior at low temperatures. However, as the temperature increases, the activation entropy starts to dominate, leading to a traditional Arrhenius behavior. We have computed the activation entropy analytically along the minimum energy path following Schoeck's methods [1], which capture the cross-over between anti-Arrhenius and Arrhenius domains. Also, the Projected Average Force Integrator (PAFI) [2], another simulation method to compute free energies along an initial transition path, exhibits considerable concurrence with Schoeck's formalism. We conclude that entropic effects need to be considered to understand processes involving dislocations bypassing elastic barriers close to the critical resolved shear stress. More work needs to be performed to fully understand the discrepancies between Schoeck's and PAFI results compared to molecular dynamics.

This paper proposes a methodology for constructing such corpora of child directed speech (CDS) paired with sentential logical forms, and uses this method to create two such corpora, in English and Hebrew. The approach enforces a cross-linguistically consistent representation, building on recent advances in dependency representation and semantic parsing. Specifically, the approach involves two steps. First, we annotate the corpora using the Universal Dependencies (UD) scheme for syntactic annotation, which has been developed to apply consistently to a wide variety of domains and typologically diverse languages. Next, we further annotate these data by applying an automatic method for transducing sentential logical forms (LFs) from UD structures. The UD and LF representations have complementary strengths: UD structures are language-neutral and support consistent and reliable annotation by multiple annotators, whereas LFs are neutral as to their syntactic derivation and transparently encode semantic relations. Using this approach, we provide syntactic and semantic annotation for two corpora from CHILDES: Brown's Adam corpus (English; we annotate ~80% of its child-directed utterances), all child-directed utterances from Berman's Hagar corpus (Hebrew). We verify the quality of the UD annotation using an inter-annotator agreement study, and manually evaluate the transduced meaning representations. We then demonstrate the utility of the compiled corpora through (1) a longitudinal corpus study of the prevalence of different syntactic and semantic phenomena in the CDS, and (2) applying an existing computational model of language acquisition to the two corpora and briefly comparing the results across languages.

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous axiomatic treatments of continuous and discrete scale-space theory, we consider three main ways discretizing these scale-space operations in terms of explicit discrete convolutions, based on either (i) sampling the Gaussian kernels and the Gaussian derivative kernels, (ii) locally integrating the Gaussian kernels and the Gaussian derivative kernels over each pixel support region and (iii) basing the scale-space analysis on the discrete analogue of the Gaussian kernel, and then computing derivative approximations by applying small-support central difference operators to the spatially smoothed image data. We study the properties of these three main discretization methods both theoretically and experimentally, and characterize their performance by quantitative measures, including the results they give rise to with respect to the task of scale selection, investigated for four different use cases, and with emphasis on the behaviour at fine scales. The results show that the sampled Gaussian kernels and derivatives as well as the integrated Gaussian kernels and derivatives perform very poorly at very fine scales. At very fine scales, the discrete analogue of the Gaussian kernel with its corresponding discrete derivative approximations performs substantially better. The sampled Gaussian kernel and the sampled Gaussian derivatives do, on the other hand, lead to numerically very good approximations of the corresponding continuous results, when the scale parameter is sufficiently large, in the experiments presented in the paper, when the scale parameter is greater than a value of about 1, in units of the grid spacing.

In logistic regression modeling, Firth's modified estimator is widely used to address the issue of data separation, which results in the nonexistence of the maximum likelihood estimate. Firth's modified estimator can be formulated as a penalized maximum likelihood estimator in which Jeffreys' prior is adopted as the penalty term. Despite its widespread use in practice, the formal verification of the corresponding estimate's existence has not been established. In this study, we establish the existence theorem of Firth's modified estimate in binomial logistic regression models, assuming only the full column rankness of the design matrix. We also discuss other binomial regression models obtained through alternating link functions and prove the existence of similar penalized maximum likelihood estimates for such models.

Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals, adding to the literature on confidence sequences (CS) -- sequences of confidence intervals that are uniformly valid over time -- which provide valid inference at arbitrary stopping times and incur no penalties for "peeking" at the data, unlike classical confidence intervals which require the sample size to be fixed in advance. Existing CSs in the literature are nonasymptotic, enjoying finite-sample guarantees but not the aforementioned broad applicability of asymptotic confidence intervals. This work provides a definition for "asymptotic CSs" and a general recipe for deriving them. Asymptotic CSs forgo nonasymptotic validity for CLT-like versatility and (asymptotic) time-uniform guarantees. While the CLT approximates the distribution of a sample average by that of a Gaussian for a fixed sample size, we use strong invariance principles (stemming from the seminal 1960s work of Strassen) to uniformly approximate the entire sample average process by an implicit Gaussian process. As an illustration, we derive asymptotic CSs for the average treatment effect in observational studies (for which nonasymptotic bounds are essentially impossible to derive even in the fixed-time regime) as well as randomized experiments, enabling causal inference in sequential environments.

Principal stratification is a popular framework for causal inference in the presence of an intermediate outcome. While the principal average treatment effects have traditionally been the default target of inference, it may not be sufficient when the interest lies in the relative favorability of one potential outcome over the other within the principal stratum. We thus introduce the principal generalized causal effect estimands, which extend the principal average causal effects to accommodate nonlinear contrast functions. Under principal ignorability, we expand the theoretical results in Jiang et. al. (2022) to a much wider class of causal estimands in the presence of a binary intermediate variable. We develop identification formulas and derive the efficient influence functions of the generalized estimands for principal stratification analyses. These efficient influence functions motivate a set of multiply robust estimators and lay the ground for obtaining efficient debiased machine learning estimators via cross-fitting based on $U$-statistics. The proposed methods are illustrated through simulations and the analysis of a data example.

Conversation demands attention. Speakers must call words to mind, listeners must make sense of them, and both together must negotiate this flow of information, all in fractions of a second. We used large language models to study how this works in a large-scale dataset of English-language conversation, the CANDOR corpus. We provide a new estimate of the information density of unstructured conversation, of approximately 13 bits/second, and find significant effects associated with the cognitive load of both retrieving, and presenting, that information. We also reveal a role for backchannels -- the brief yeahs, uh-huhs, and mhmms that listeners provide -- in regulating the production of novelty: the lead-up to a backchannel is associated with declining information rate, while speech downstream rebounds to previous rates. Our results provide new insights into long-standing theories of how we respond to fluctuating demands on cognitive resources, and how we negotiate those demands in partnership with others.

We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional nonlinear Bayesian inverse problems. While geometric MCMC employs high-quality proposals that adapt to posterior local geometry, it requires computing local gradient and Hessian information of the log-likelihood, incurring a high cost when the parameter-to-observable (PtO) map is defined through expensive model simulations. We consider a delayed-acceptance geometric MCMC method driven by a neural operator surrogate of the PtO map, where the proposal is designed to exploit fast surrogate approximations of the log-likelihood and, simultaneously, its gradient and Hessian. To achieve a substantial speedup, the surrogate needs to be accurate in predicting both the observable and its parametric derivative (the derivative of the observable with respect to the parameter). Training such a surrogate via conventional operator learning using input--output samples often demands a prohibitively large number of model simulations. In this work, we present an extension of derivative-informed operator learning [O'Leary-Roseberry et al., J. Comput. Phys., 496 (2024)] using input--output--derivative training samples. Such a learning method leads to derivative-informed neural operator (DINO) surrogates that accurately predict the observable and its parametric derivative at a significantly lower training cost than the conventional method. Cost and error analysis for reduced basis DINO surrogates are provided. Numerical studies on PDE-constrained Bayesian inversion demonstrate that DINO-driven MCMC generates effective posterior samples 3--9 times faster than geometric MCMC and 60--97 times faster than prior geometry-based MCMC. Furthermore, the training cost of DINO surrogates breaks even after collecting merely 10--25 effective posterior samples compared to geometric MCMC.

Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.