Unmanned aerial vehicle (UAV) photogrammetry allows for the creation of orthophotos and digital surface models (DSMs) of a terrain. However, DSMs of water bodies mapped with this technique reveal water surface distortions, preventing the use of photogrammetric data for accurate determination of water surface elevation (WSE). Firstly, we propose a new solution in which a convolutional neural network (CNN) is used as a WSE estimator from photogrammetric DSMs and orthophotos. Second, we improved the previously known "water-edge" method by filtering the outliers using a forward-backwards exponential weighted moving average. Further improvement in these two methods was achieved by performing a linear regression of the WSE values against chainage. The solutions estimate the uncertainty of the predictions. This is the first approach in which DL was used for this task. A brand new machine learning data set has been created. It was collected on a small lowland river in winter and summer conditions. It consists of 322 samples, each corresponding to a 10 by 10 meter area of the river channel and adjacent land. Each data set sample contains orthophoto and DSM arrays as input, along with a single ground-truth WSE value as output. The data set was supplemented with data collected by other researchers that compared the state-of-the-art methods for determining WSE using an UAV. The results of the DL solution were verified using k-fold cross-validation method. This provided an in-depth examination of the model's ability to perform on previously unseen data. The WSE RMSEs differ for each k-fold cross-validation subset and range from 1.7 cm up to 17.2 cm. The RMSE results of the improved "water-edge" method are at least six times lower than the RMSE results achieved by the conventional "water-edge" method. The results obtained by new methods are predominantly outperforming existing ones.

We argue that for analysis of Positive Unlabeled (PU) data under Selected Completely At Random (SCAR) assumption it is fruitful to view the problem as fitting of misspecified model to the data. Namely, we show that the results on misspecified fit imply that in the case when posterior probability of the response is modelled by logistic regression, fitting the logistic regression to the observable PU data which {\it does not} follow this model, still yields the vector of estimated parameters approximately colinear with the true vector of parameters. This observation together with choosing the intercept of the classifier based on optimisation of analogue of F1 measure yields a classifier which performs on par or better than its competitors on several real data sets considered.

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.

Traffic prediction plays a crucial role in alleviating traffic congestion which represents a critical problem globally, resulting in negative consequences such as lost hours of additional travel time and increased fuel consumption. Integrating emerging technologies into transportation systems provides opportunities for improving traffic prediction significantly and brings about new research problems. In order to lay the foundation for understanding the open research challenges in traffic prediction, this survey aims to provide a comprehensive overview of traffic prediction methodologies. Specifically, we focus on the recent advances and emerging research opportunities in Artificial Intelligence (AI)-based traffic prediction methods, due to their recent success and potential in traffic prediction, with an emphasis on multivariate traffic time series modeling. We first provide a list and explanation of the various data types and resources used in the literature. Next, the essential data preprocessing methods within the traffic prediction context are categorized, and the prediction methods and applications are subsequently summarized. Lastly, we present primary research challenges in traffic prediction and discuss some directions for future research.

Conditional Average Treatment Effects (CATE) estimation is one of the main challenges in causal inference with observational data. In addition to Machine Learning based-models, nonparametric estimators called meta-learners have been developed to estimate the CATE with the main advantage of not restraining the estimation to a specific supervised learning method. This task becomes, however, more complicated when the treatment is not binary as some limitations of the naive extensions emerge. This paper looks into meta-learners for estimating the heterogeneous effects of multi-valued treatments. We consider different meta-learners, and we carry out a theoretical analysis of their error upper bounds as functions of important parameters such as the number of treatment levels, showing that the naive extensions do not always provide satisfactory results. We introduce and discuss meta-learners that perform well as the number of treatments increases. We empirically confirm the strengths and weaknesses of those methods with synthetic and semi-synthetic datasets.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. Here we consider estimating which data values are incorrect along a numerical column. We present a model-agnostic approach that can utilize any regressor (i.e. statistical or machine learning model) which was fit to predict values in this column based on the other variables in the dataset. By accounting for various uncertainties, our approach distinguishes between genuine anomalies and natural data fluctuations, conditioned on the available information in the dataset. We establish theoretical guarantees for our method and show that other approaches like conformal inference struggle to detect errors. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

It is widely believed that given the same labeling budget, active learning (AL) algorithms like margin-based active learning achieve better predictive performance than passive learning (PL), albeit at a higher computational cost. Recent empirical evidence suggests that this added cost might be in vain, as margin-based AL can sometimes perform even worse than PL. While existing works offer different explanations in the low-dimensional regime, this paper shows that the underlying mechanism is entirely different in high dimensions: we prove for logistic regression that PL outperforms margin-based AL even for noiseless data and when using the Bayes optimal decision boundary for sampling. Insights from our proof indicate that this high-dimensional phenomenon is exacerbated when the separation between the classes is small. We corroborate this intuition with experiments on 20 high-dimensional datasets spanning a diverse range of applications, from finance and histology to chemistry and computer vision.

We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new measurement, a consensus term taking a weighted sum of estimations of its own and its neighbors with additive and multiplicative communication noises and a regularization term preventing over-fitting. It is not required that the regression matrices and graphs satisfy special statistical assumptions such as mutual independence, spatio-temporal independence or stationarity. We develop the nonnegative supermartingale inequality of the estimation error, and prove that the estimations of all nodes converge to the unknown true parameter vector almost surely if the algorithm gains, graphs and regression matrices jointly satisfy the sample path spatio-temporal persistence of excitation condition. Especially, this condition holds by choosing appropriate algorithm gains if the graphs are uniformly conditionally jointly connected and conditionally balanced, and the regression models of all nodes are uniformly conditionally spatio-temporally jointly observable, under which the algorithm converges in mean square and almost surely. In addition, we prove that the regret upper bound is $O(T^{1-\tau}\ln T)$, where $\tau\in (0.5,1)$ is a constant depending on the algorithm gains.

Active learning seeks to reduce the amount of data required to fit the parameters of a model, thus forming an important class of techniques in modern machine learning. However, past work on active learning has largely overlooked latent variable models, which play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines. Here we address this gap by proposing a novel framework for maximum-mutual-information input selection for discrete latent variable regression models. We first apply our method to a class of models known as "mixtures of linear regressions" (MLR). While it is well known that active learning confers no advantage for linear-Gaussian regression models, we use Fisher information to show analytically that active learning can nevertheless achieve large gains for mixtures of such models, and we validate this improvement using both simulations and real-world data. We then consider a powerful class of temporally structured latent variable models given by a Hidden Markov Model (HMM) with generalized linear model (GLM) observations, which has recently been used to identify discrete states from animal decision-making data. We show that our method substantially reduces the amount of data needed to fit GLM-HMM, and outperforms a variety of approximate methods based on variational and amortized inference. Infomax learning for latent variable models thus offers a powerful for characterizing temporally structured latent states, with a wide variety of applications in neuroscience and beyond.

One straightforward metric to evaluate a survival prediction model is based on the Mean Absolute Error (MAE) -- the average of the absolute difference between the time predicted by the model and the true event time, over all subjects. Unfortunately, this is challenging because, in practice, the test set includes (right) censored individuals, meaning we do not know when a censored individual actually experienced the event. In this paper, we explore various metrics to estimate MAE for survival datasets that include (many) censored individuals. Moreover, we introduce a novel and effective approach for generating realistic semi-synthetic survival datasets to facilitate the evaluation of metrics. Our findings, based on the analysis of the semi-synthetic datasets, reveal that our proposed metric (MAE using pseudo-observations) is able to rank models accurately based on their performance, and often closely matches the true MAE -- in particular, is better than several alternative methods.