相关论文: Simpler and Better Cardinality Estimators for Hype…

Understanding the morphology of galaxies is a critical aspect of astrophysics research, providing insight into the formation, evolution, and physical properties of these vast cosmic structures. Various observational and computational…

Weak lensing statistics is typically measured as weighted sum of shear estimators or their products (shear-shear correlation). The weighting schemes are designed in the hope of minimizing the statistical error without introducing systematic…

Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…

Many problems in high-dimensional statistics appear to have a statistical-computational gap: a range of values of the signal-to-noise ratio where inference is information-theoretically possible, but (conjecturally) computationally…

The partial correlation graphical LASSO (PCGLASSO) is a penalised likelihood method for Gaussian graphical models which provides scale invariant sparse estimation of the precision matrix and improves upon the popular graphical LASSO method.…

With the increasing popularity of large language models (LLMs), reasoning on basic graph algorithm problems is an essential intermediate step in assessing their abilities to process and infer complex graph reasoning tasks. Existing methods…

Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…

With the rapid increase in volume of time series medical data available through wearable devices, there is a need to employ automated algorithms to label data. Examples of labels include interventions, changes in activity (e.g. sleep) and…

Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality…

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

MinHash and HyperLogLog are sketching algorithms that have become indispensable for set summaries in big data applications. While HyperLogLog allows counting different elements with very little space, MinHash is suitable for the fast…

With the rapidly improving reasoning abilities of Large Language Models (LLMs), there is also a rising demand to use them in a wide variety of domains. This brings about the need to carefully evaluate the limits of the capabilities of these…

This paper presents a distributed estimator for a deterministic parametric physical field sensed by a homogeneous sensor network and develops a new transformed expression for the Cramer-Rao lower bound (CRLB) on the variance of distributed…

We seek to address a core challenge facing current Large Language Models (LLMs). LLMs have demonstrated superior performance in many tasks, yet continue to struggle with reasoning problems on explicit graphs that require multiple steps. To…

This PhD thesis lays out algebraic and topological structures relevant for the study of probabilistic graphical models. Marginal estimation algorithms are introduced as diffusion equations of the form $\dot u = \delta \varphi$. They…

Differentiating signals from the background in micrographs is a critical initial step for cryogenic electron microscopy (cryo-EM), yet it remains laborious due to low signal-to-noise ratio (SNR), the presence of contaminants and densely…

Principal component pursuit (PCP) is a state-of-the-art approach for background estimation problems. Due to their higher computational cost, PCP algorithms, such as robust principal component analysis (RPCA) and its variants, are not…

We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by…

Parameter estimation in ordinary differential equations, although applied and refined in various fields of the quantitative sciences, is still confronted with a variety of difficulties. One major challenge is finding the global optimum of a…

The multi-scale entanglement renormalization ansatz (MERA) provides a natural description of the ground state of a quantum critical Hamiltonian on the lattice. From an optimized MERA, one can extract the scaling dimensions of the underlying…