Related papers: The Causal Bootstrap: Bounding Smeared Spectral Fu…

We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject…

To draw scientifically meaningful conclusions and build reliable models of quantitative phenomena, cause and effect must be taken into consideration (either implicitly or explicitly). This is particularly challenging when the measurements…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. While traditionally studied within Euclidean spaces, contemporary applications…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Causal effect estimation is important for many tasks in the natural and social sciences. We design algorithms for the continuous partial identification problem: bounding the effects of multivariate, continuous treatments when unmeasured…

Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while…

Machine learning models achieve state-of-the-art performance on many supervised learning tasks. However, prior evidence suggests that these models may learn to rely on shortcut biases or spurious correlations (intuitively, correlations that…

The identification of causal effects in observational studies typically relies on two standard assumptions: unconfoundedness and overlap. However, both assumptions are often questionable in practice: unconfoundedness is inherently…

Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…

Despite the success of deep learning in dermoscopy image analysis, its inherent black-box nature hinders clinical trust, motivating the use of prototypical networks for case-based visual transparency. However, inevitable selection bias in…

Due to the challenge posed by multi-source and heterogeneous data collected from diverse environments, causal relationships among features can exhibit variations influenced by different time spans, regions, or strategies. This diversity…

In the spatial point process context, kernel intensity estimation has been mainly restricted to exploratory analysis due to its lack of consistency. Different methods have been analysed to overcome this problem, and the inclusion of…

Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…

In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given…

Various physical quantities -- including real-time response, inclusive cross-sections, and decay rates -- may not be directly determined from Euclidean correlators. They are, however, easily determined from the spectral density, motivating…

Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…

In experimental causal inference, we distinguish between two sources of uncertainty: design uncertainty, due to the treatment assignment mechanism, and sampling uncertainty, when the sample is drawn from a super-population. This distinction…

Estimating causal effects from large experimental and observational data has become increasingly prevalent in both industry and research. The bootstrap is an intuitive and powerful technique used to construct standard errors and confidence…

We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…