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We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…
Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…
Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal…
In a recent paper (Efron (2004)), Efron pointed out that an important issue in large-scale multiple hypothesis testing is that the null distribution may be unknown and need to be estimated. Consider a Gaussian mixture model, where the null…
We develop novel LASSO-based methods for coefficient testing and confidence interval construction in the Gaussian linear model with $n\ge d$. Our methods' finite-sample validity is identical to that of their ubiquitous…
Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail…
The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…
This paper introduces a novel Perturbation-Assisted Inference (PAI) framework utilizing synthetic data generated by the Perturbation-Assisted Sample Synthesis (PASS) method. The framework focuses on uncertainty quantification in complex…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
In the common time series model $X_{i,n} = \mu (i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $\mu$ from a benchmark $g (\mu )$ (such as the initial…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…
Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of confidence interval procedures based solely on…
The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…
This article introduces exact testing procedures on the mean of a Gaussian process $X$ derived from the outcomes of $\ell_1$-minimization over the space of complex valued measures. The process $X$ can be thought as the sum of two terms:…
Let $\mu$ be a Gaussian measure (say, on ${\bf R}^n$) and let $K, L \subset {\bf R}^n$ be such that K is convex, $L$ is a "layer" (i.e. $L = \{x : a \leq < x,u > \leq b \}$ for some $a$, $b \in {\bf R}$ and $u \in {\bf R}^n$) and the…
We give new proofs of certain equivalent conditions for the existence of generalized moments of a L\'evy process $(X_t)_{t\geq 0}$; in particular, the existence of a generalized $g$-moment is equivalent to the uniform integrability of…