Miracle-dz/UniFAR-FTUs huggingface dataset:
Revisiting Local Descriptor Based Image-To-Class Measure for Few-Shot Learning

Few-shot learning in image classification aims to learn a classifier to classify images when only few training examples are available for each class. Recent work has achieved promising classification performance, where an image-level feature based measure is usually used. In this paper, we argue that a measure at such a level may not be effective enough in light of the scarcity of examples in few-shot learning. Instead, we think a local descriptor based image-to-class measure should be taken, inspired by its surprising success in the heydays of local invariant features. Specifically, building upon the recent episodic training mechanism, we propose a Deep Nearest Neighbor Neural Network (DN4 in short) and train it in an end-to-end manner. Its key difference from the literature is the replacement of the image-level feature based measure in the final layer by a local descriptor based image-to-class measure. This measure is conducted online via a k-nearest neighbor search over the deep local descriptors of convolutional feature maps. The proposed DN4 not only learns the optimal deep local descriptors for the image-to-class measure, but also utilizes the higher efficiency of such a measure in the case of example scarcity, thanks to the exchangeability of visual patterns across the images in the same class. Our work leads to a simple, effective, and computationally efficient framework for few-shot learning. Experimental study on benchmark datasets consistently shows its superiority over the related state-of-the-art, with the largest absolute improvement of 17% over the next best. The source code can be available from https://github.com/WenbinLee/DN4.git.
What is meant by 'P(R|Yobs)'?

Missing at Random (MAR) is a central concept in incomplete data methods, and often it is stated as $P(R\mspace{3mu}|\,Y_{obs}, Y_{mis}) = P(R\mspace{3mu}|\,Y_{obs})$. This notation has been used in the literature for more than three decades and has become the de facto standard. In some cases, the notation has been misinterpreted to be a statement about conditional independence. While previous work has sought to clarify the required definitions, a clear explanation of how to interpret the standard notation is lacking, and a definition of the function $P(R\mspace{3mu}|\,Y_{obs})$ for non-MAR mechanisms is difficult to locate in the literature. The aim of this paper is to fill these gaps.
Finite and infinite Mallows ranking models, maximum likelihood estimator, and regeneration

In this paper we are concerned with various Mallows ranking models. First we study the statistical properties of the MLE of Mallows' $\phi$ model: $\mathbb{P}_{\theta, \pi_0}(\pi) \propto \exp(-\theta \, inv(\pi \circ \pi_0^{-1}))$, where $\theta$ is the dispersion parameter and $\pi_0$ is the central ranking. We prove that (1). the MLE $\widehat{\theta}$ is biased upwards for both Mallows' $\phi$ model and the single parameter IGM model; (2). the MLE $\widehat{\pi}_0$ converges exponentially for Mallows' $\phi$ model. We also make connections of various Mallows ranking models, encompassing the work of Gnedin and Olshanski, and Pitman and Tang. Motivated by the infinite top-$t$ ranking model of Meilǎ and Bao, we propose an algorithm to select the model size $t$ automatically. The key idea relies on the regenerative property of such an infinite permutation. Finally, we apply our algorithm to several data sets including the APA election data and the University homepage search data.
An Adaptive Grid Algorithm for Computing the Homology Group of Semialgebraic Set

Looking for an efficient algorithm for the computation of the homology groups of an algebraic set or even a semi-algebraic set is an important problem in the effective real algebraic geometry. Recently, Peter Burgisser, Felipe Cucker and Pierre Lairez wrote a paper [1], which made a step forward by giving an algorithm of weak exponential time. However, the algorithm is not not practical. In my thesis, I will introduce my improvement of this algorithm using an adaptive grid algorithm on the unit sphere.
Detecting British Columbia coastal rainfall patterns by clustering Gaussian processes

Functional data analysis is a statistical framework where data are assumed to follow some functional form. This method of analysis is commonly applied to time series data, where time, measured continuously or in discrete intervals, serves as the location for a function's value. Gaussian processes are a generalization of the multivariate normal distribution to function space and, in this article, they are used to shed light on coastal rainfall patterns in British Columbia (BC). Specifically, this work addressed the question over how one should carry out an exploratory cluster analysis for the BC, or any similar, coastal rainfall data. An approach is developed for clustering multiple processes observed on a comparable interval, based on how similar their underlying covariance kernel is. This approach provides interesting insights into the BC data, and these insights can be framed in terms of Pacific Ocean temperatures. From one perspective, the results show that clustering annual rainfall can potentially be used to identify extreme weather patterns.
Efficient Marginalization-Based MCMC Methods for Hierarchical Bayesian Inverse Problems

Hierarchical models in Bayesian inverse problems are characterized by an assumed prior probability distribution for the unknown state and measurement error precision, and hyper-priors for the prior parameters. Combining these probability models using Bayes' law often yields a posterior distribution that cannot be sampled from directly, even for a linear model with Gaussian measurement error and Gaussian prior. Gibbs sampling can be used to sample from the posterior, but problems arise when the dimension of the state is large. This is because the Gaussian sample required for each iteration can be prohibitively expensive to compute, and because the statistical efficiency of the Markov chain degrades as the dimension of the state increases. The latter problem can be mitigated using marginalization-based techniques, but these can be computationally prohibitive as well. In this paper, we combine the low-rank techniques of Brown, Saibaba, and Vallelian (2018) with the marginalization approach of Rue and Held (2005). We consider two variants of this approach: delayed acceptance and pseudo-marginalization. We provide a detailed analysis of the acceptance rates and computational costs associated with our proposed algorithms, and compare their performances on two numerical test cases---image deblurring and inverse heat equation.
A Data-driven Approach to Multi-event Analytics in Large-scale Power Systems Using Factor Model

Multi-event detection and recognition in real time is of challenge for a modern grid as its feature is usually non-identifiable. Based on factor model, this paper porposes a data-driven method as an alternative solution under the framework of random matrix theory. This method maps the raw data into a high-dimensional space with two parts: 1) the principal components (factors, mapping event signals); and 2) time series residuals (bulk, mapping white/non-Gaussian noises). The spatial information is extracted form factors, and the termporal infromation from residuals. Taking both spatial-tempral correlation into account, this method is able to reveal the multi-event: its components and their respective details, e.g., occurring time. Case studies based on the standard IEEE 118-bus system validate the proposed method.
Revisiting the Gelman–Rubin Diagnostic

Gelman and Rubin's (1992) convergence diagnostic is one of the most popular methods for terminating a Markov chain Monte Carlo (MCMC) sampler. Since the seminal paper, researchers have developed sophisticated methods for estimating variance of Monte Carlo averages. We show that these estimators find immediate use in the Gelman-Rubin statistic, a connection not previously established in the literature. We incorporate these estimators to upgrade both the univariate and multivariate Gelman-Rubin statistics, leading to improved stability in MCMC termination time. An immediate advantage is that our new Gelman-Rubin statistic can be calculated for a single chain. In addition, we establish a one-to-one relationship between the Gelman-Rubin statistic and effective sample size. Leveraging this relationship, we develop a principled termination criterion for the Gelman-Rubin statistic. Finally, we demonstrate the utility of our improved diagnostic via examples.
Acid Stress Triggers Resistance to Acetic Acid-Induced Regulated Cell Death through Hog1 Activation Which Requires RTG2 in Yeast

Acid stress causes resistance to acetic acid-induced regulated cell death (AA-RCD) in budding yeast, resulting in catalase activation. In order to explore the molecular determinants of evasion of AA-RCD triggered by acid stress adaptation, we studied the involvement and the possible interplay of the master regulator of transcription high-osmolarity glycerol 1 (HOG1) and RTG2, a positive regulator of the RTG-dependent mitochondrial retrograde signaling. Viability, DNA fragmentation, and ROS accumulation have been analyzed in wild-type and mutant cells lacking HOG1 and/or RTG2. Catalase activity and transcription of CTT1 and CTA1, coding the cytosolic and peroxisomal/mitochondrial catalase, respectively, as well as Hog1 phosphorylation, were also analyzed. Our results show that HOG1 is essential for resistance to AA-RCD and its activation results in the upregulation of CTT1, but not CTA1, transcription during acid stress adaptation. RTG2 is required for Hog1-dependent CTT1 upregulation upon acid stress, despite failure of RTG pathway activation. We give evidence that Rtg2 has a cytoprotective role and can act as a general cell stress sensor independent of Rtg1/3-dependent transcription.
A comparative study of estimation methods in quantum tomography

As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum likelihood, least squares, generalised least squares, positive least squares, thresholded least squares and projected least squares. The common thread of the analysis is that each estimator projects the measurement data onto a parameter space with respect to a specific metric, thus allowing us to study the relationships between different estimators. The asymptotic behaviour of the least squares and the projected least squares estimators is studied in detail for the case of the covariant measurement and a family of states of varying ranks. This gives insight into the rank-dependent risk reduction for the projected estimator, and uncovers an interesting non-monotonic behaviour of the Bures risk. These asymptotic results complement recent non-asymptotic concentration bounds of Guta et al (2018 (arXiv:1809.11162)) which point to strong optimality properties, and high computational efficiency of the projected linear estimators. To illustrate the theoretical methods we present results of an extensive simulation study. An app running the different estimators has been made available online.
Frowning Frodo, Wincing Leia, and a Seriously Great Friendship: Learning to Classify Emotional Relationships of Fictional Characters

The development of a fictional plot is centered around characters who closely interact with each other forming dynamic social networks. In literature analysis, such networks have mostly been analyzed without particular relation types or focusing on roles which the characters take with respect to each other. We argue that an important aspect for the analysis of stories and their development is the emotion between characters. In this paper, we combine these aspects into a unified framework to classify emotional relationships of fictional characters. We formalize it as a new task and describe the annotation of a corpus, based on fan-fiction short stories. The extraction pipeline which we propose consists of character identification (which we treat as given by an oracle here) and the relation classification. For the latter, we provide results using several approaches previously proposed for relation identification with neural methods. The best result of 0.45 F1 is achieved with a GRU with character position indicators on the task of predicting undirected emotion relations in the associated social network graph.
Non-Asymptotic Chernoff Lower Bound and Its Application to Community Detection in Stochastic Block Model.

Chernoff coefficient is an upper bound of Bayes error probability in classification problem. In this paper, we will develop sharp Chernoff type bound on Bayes error probability. The new bound is not only an upper bound but also a lower bound of Bayes error probability up to a constant in a non-asymptotic setting. Moreover, we will apply this result to community detection in stochastic block model. As a clustering problem, the optimal error rate of community detection can be characterized by our Chernoff type bound. This can be formalized by deriving a minimax error rate over certain class of parameter space, then achieving such error rate by a feasible algorithm employ multiple steps of EM type updates.
Implementation and Validation of an Analytical Method for Lincomycin Determination in Feathers and Edible Tissues of Broiler Chickens by Liquid Chromatography Tandem Mass Spectrometry

Recent studies have detected different antimicrobial residues in broiler chicken feathers, where they persisted for longer periods of time and at greater concentrations than in edible tissues. However, until today, lincomycin behaviour in this nonedible tissue has not been assessed yet. Considering this, an analytical methodology to detect and quantify this antibiotic concentration in feathers, muscle, and liver tissues from broiler chickens was implemented and in-house validated. The methodology will allow the determination of the bioaccumulation of this highly persistent antibiotic in feathers of treated birds. For this purpose, 98% lincomycin and 95% lincomycin D3 standards were used. Methanol was selected as the extraction solvent, and Chromabond® Florisil® cartridges were used for the clean-up stage. The separation of analytes was performed through the analytical column SunFire C18 with a running time of 4 minutes, and the instrumental analysis was performed through an LC-MS/MS, with a liquid chromatograph Agilent® 1290 Infinity, coupled to an AB SCIEX® API 5500 mass spectrometer. An internal protocol for an in-house validation was designed based on recommendations from Commission Decision 2002/657/EC and the Guidance document on the estimation of limit of detection and limit of quantification for measurements in the field of contaminants in feed and food. The average retention time for lincomycin was 2.255 min (for quantifier ion, 126.0). The calibration curves showed a coefficient of determination (r2) greater than 0.99 for all matrices, while recovery levels ranged between 98% and 101%. The limit of detection (LOD) calculated was of 19, 22, and 10 μg·kg−1, and the limit of quantification (LOQ) was of 62, 73, and 34 μg·kg−1 in feathers, muscle, and liver, respectively. This method detects lincomycin in the studied matrices, confidently and accurately, as it is required for designing analytical studies of drug residues in edible and nonedible tissues, such as feathers.
Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence

Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC functions have been extensively studied, stochastic optimization that is more suitable for learning with big data remains under-explored. In this paper, we propose new stochastic optimization algorithms and study their first-order convergence theories for solving a broad family of DC functions. We improve the existing algorithms and theories of stochastic optimization for DC functions from both practical and theoretical perspectives. On the practical side, our algorithm is more user-friendly without requiring a large mini-batch size and more efficient by saving unnecessary computations. On the theoretical side, our convergence analysis does not necessarily require the involved functions to be smooth with Lipschitz continuous gradient. Instead, the convergence rate of the proposed stochastic algorithm is automatically adaptive to the H\"{o}lder continuity of the gradient of one component function. Moreover, we extend the proposed stochastic algorithms for DC functions to solve problems with a general non-convex non-differentiable regularizer, which does not necessarily have a DC decomposition but enjoys an efficient proximal mapping. To the best of our knowledge, this is the first work that gives the first non-asymptotic convergence for solving non-convex optimization whose objective has a general non-convex non-differentiable regularizer.
An innovating Statistical Learning Tool based on Partial Differential Equations, intending livestock Data Assimilation

The realistic modeling intended to quantify precisely some biological mechanisms is a task requiering a lot of a priori knowledge and generally leading to heavy mathematical models. On the other hand, the structure of the classical Machine Learning algorithms, such as Neural Networks, limits their flexibility and the possibility to take into account the existence of complex underlying phenomena, such as delay, saturation and accumulation. The aim of this paper is to reach a compromise between precision, parsimony and flexibility to design an efficient biomimetic predictive tool extracting knowledge from livestock data. To achieve this, we build a Mathematical Model based on Partial Differential Equations (PDE) embarking the mathematical expression of biological determinants. We made the hypothesis that all the physico-chemical phenomena occurring in animal body can be summarized by the evolution of a global information. Therefore the developed PDE system describes the evolution and the action of an information circulating in an Avatar of the Real Animal. This Avatar outlines the dynamics of the biological reactions of animal body in the framework of a specific problem. Each PDE contains parameters corresponding to biological-like factors which can be learnt from data by the developed Statistical Learning Tool.
Multiple testing for outlier detection in functional data

We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA). A multiple testing procedure based on the two-sample test is defined in order to highlight the levels of the coefficients on which the outliers appear as significantly different to the normal data. The selected coefficients are then called features for the outlier detection, on which we compute the Local Outlier Factor to highlight the outliers. This procedure to select the features is applied on simulated data that mimic the behaviour of space telemetries, and compared with existing dimension reduction techniques.
A pliable lasso for the Cox model

We introduce a pliable lasso method for estimation of interaction effects in the Cox proportional hazards model framework. The pliable lasso is a linear model that includes interactions between covariates X and a set of modifying variables Z and assumes sparsity of the main effects and interaction effects. The hierarchical penalty excludes interaction effects when the corresponding main effects are zero: this avoids overfitting and an explosion of model complexity. We extend this method to the Cox model for survival data, incorporating modifiers that are either fixed or varying in time into the partial likelihood. For example, this allows modeling of survival times that differ based on interactions of genes with age, gender, or other demographic information. The optimization is done by blockwise coordinate descent on a second order approximation of the objective.
On ideal triangulations of surfaces up to branched transit equivalences

We consider triangulations of closed surfaces S with a given set of vertices V; every triangulation can be branched that is enhanced to a Delta-complex. Branched triangulations are considered up to the b-transit equivalence generated by b-flips (i.e. branched diagonal exchanges) and isotopy keeping V point-wise fixed. We extend a well known connectivity result for `naked' triangulations; in particular in the generic case when S has negative Euler-Poincare' characteristic c(S), we show that branched triangulations are equivalent to each other if c(S) is even, while this holds also for odd c(S) possibly after the complete inversion of one of the two branchings. Moreover we show that under a mild assumption, two branchings on a same triangulation are connected via a sequence of inversions of ambiguous edges (and possibly the total inversion of one of them). A natural organization of the b-flips in subfamilies gives rise to restricted transit equivalences with non trivial (even infinite) quotient sets. We analyze them in terms of certain preserved structures of differential topological nature carried by any branched triangulations; in particular a pair of transverse foliations with determined singular sets contained in V, including as particular cases the configuration of the vertical and horizontal foliations of the square of an Abelian differential on a Riemann surface.
Transport Map Accelerated Adaptive Importance Sampling, and Application to Inverse Problems Arising from Multiscale Stochastic Reaction Networks

In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower dimensional manifolds on which the likelihood function is invariant, or varies very little. This can be due to trying to infer unobservable parameters, or due to sloppiness in the model which is being used to describe the data. In such a situation, standard sampling methods for characterising the posterior distribution, which do not incorporate information about this structure, will be highly inefficient. In this paper, we seek to develop an approach to tackle this problem when using adaptive importance sampling methods, by using optimal transport maps to simplify posterior distributions which are concentrated on lower dimensional manifolds. This approach is applicable to a whole range of problems for which Monte Carlo Markov chain (MCMC) methods mix slowly. We demonstrate the approach by considering inverse problems arising from partially observed stochastic reaction networks. In particular, we consider systems which exhibit multiscale behaviour, but for which only the slow variables in the system are observable. We demonstrate that certain multiscale approximations lead to more consistent approximations of the posterior than others. The use of optimal transport maps stabilises the ensemble transform adaptive importance sampling (ETAIS) method, and allows for efficient sampling with smaller ensemble sizes. This approach allows us to take advantage of the large increases of efficiency when using adaptive importance sampling methods for previously intractable Bayesian inverse problems with complex posterior structure.