We propose a framework for the assessment of uncertainty quantification in deep regression. The framework is based on regression problems where the regression function is a linear combination of nonlinear functions. Basically, any level of complexity can be realized through the choice of the nonlinear functions and the dimensionality of their domain. Results of an uncertainty quantification for deep regression are compared against those obtained by a statistical reference method. The reference method utilizes knowledge of the underlying nonlinear functions and is based on a Bayesian linear regression using a reference prior. Reliability of uncertainty quantification is assessed in terms of coverage probabilities, and accuracy through the size of calculated uncertainties. We illustrate the proposed framework by applying it to current approaches for uncertainty quantification in deep regression. The flexibility, together with the availability of a reference solution, makes the framework suitable for defining benchmark sets for uncertainty quantification.

It is important to estimate the local average treatment effect (LATE) when compliance with a treatment assignment is incomplete. The previously proposed methods for LATE estimation required all relevant variables to be jointly observed in a single dataset; however, it is sometimes difficult or even impossible to collect such data in many real-world problems for technical or privacy reasons. We consider a novel problem setting in which LATE, as a function of covariates, is nonparametrically identified from the combination of separately observed datasets. For estimation, we show that the direct least squares method, which was originally developed for estimating the average treatment effect under complete compliance, is applicable to our setting. However, model selection and hyperparameter tuning for the direct least squares estimator can be unstable in practice since it is defined as a solution to the minimax problem. We then propose a weighted least squares estimator that enables simpler model selection by avoiding the minimax objective formulation. Unlike the inverse probability weighted (IPW) estimator, the proposed estimator directly uses the pre-estimated weight without inversion, avoiding the problems caused by the IPW methods. We demonstrate the effectiveness of our method through experiments using synthetic and real-world datasets.

Although the values of individual soccer players have become astronomical, subjective judgments still play a big part in the player analysis. Recently, there have been new attempts to quantitatively grasp players' styles using video-based event stream data. However, they have some limitations in scalability due to high annotation costs and sparsity of event stream data. In this paper, we build a triplet network named 6MapNet that can effectively capture the movement styles of players using in-game GPS data. Without any annotation of soccer-specific actions, we use players' locations and velocities to generate two types of heatmaps. Our subnetworks then map these heatmap pairs into feature vectors whose similarity corresponds to the actual similarity of playing styles. The experimental results show that players can be accurately identified with only a small number of matches by our method.

The model selection problem in the pure exploration linear bandit setting is introduced and studied in both the fixed confidence and fixed budget settings. The model selection problem considers a nested sequence of hypothesis classes of increasing complexities. Our goal is to automatically adapt to the instance-dependent complexity measure of the smallest hypothesis class containing the true model, rather than suffering from the complexity measure related to the largest hypothesis class. We provide evidence showing that a standard doubling trick over dimension fails to achieve the optimal instance-dependent sample complexity. Our algorithms define a new optimization problem based on experimental design that leverages the geometry of the action set to efficiently identify a near-optimal hypothesis class. Our fixed budget algorithm uses a novel application of a selection-validation trick in bandits. This provides a new method for the understudied fixed budget setting in linear bandits (even without the added challenge of model selection). We further generalize the model selection problem to the misspecified regime, adapting our algorithms in both fixed confidence and fixed budget settings.

Compositional data are non-negative data collected in a rectangular matrix with a constant row sum. Due to the non-negativity the focus is on conditional proportions that add up to 1 for each row. A row of conditional proportions is called an observed budget. Latent budget analysis (LBA) assumes a mixture of latent budgets that explains the observed budgets. LBA is usually fitted to a contingency table, where the rows are levels of one or more explanatory variables and the columns the levels of a response variable. In prospective studies, there is only knowledge about the explanatory variables of individuals and interest goes out to predicting the response variable. Thus, a form of LBA is needed that has the functionality of prediction. Previous studies proposed a constrained neural network (NN) extension of LBA that was hampered by an unsatisfying prediction ability. Here we propose LBA-NN, a feed forward NN model that yields a similar interpretation to LBA but equips LBA with a better ability of prediction. A stable and plausible interpretation of LBA-NN is obtained through the use of importance plots and table, that show the relative importance of all explanatory variables on the response variable. An LBA-NN-K- means approach that applies K-means clustering on the importance table is used to produce K clusters that are comparable to K latent budgets in LBA. Here we provide different experiments where LBA-NN is implemented and compared with LBA. In our analysis, LBA-NN outperforms LBA in prediction in terms of accuracy, specificity, recall and mean square error. We provide open-source software at GitHub.

Statistical learning additions to physically derived mathematical models are gaining traction in the literature. A recent approach has been to augment the underlying physics of the governing equations with data driven Bayesian statistical methodology. Coined statFEM, the method acknowledges a priori model misspecification, by embedding stochastic forcing within the governing equations. Upon receipt of additional data, the posterior distribution of the discretised finite element solution is updated using classical Bayesian filtering techniques. The resultant posterior jointly quantifies uncertainty associated with the ubiquitous problem of model misspecification and the data intended to represent the true process of interest. Despite this appeal, computational scalability is a challenge to statFEM's application to high-dimensional problems typically experienced in physical and industrial contexts. This article overcomes this hurdle by embedding a low-rank approximation of the underlying dense covariance matrix, obtained from the leading order modes of the full-rank alternative. Demonstrated on a series of reaction-diffusion problems of increasing dimension, using experimental and simulated data, the method reconstructs the sparsely observed data-generating processes with minimal loss of information, in both posterior mean and the variance, paving the way for further integration of physical and probabilistic approaches to complex systems.

In this work, we establish risk bounds for the Empirical Risk Minimization (ERM) with both dependent and heavy-tailed data-generating processes. We do so by extending the seminal works of Mendelson [Men15, Men18] on the analysis of ERM with heavy-tailed but independent and identically distributed observations, to the strictly stationary exponentially $\beta$-mixing case. Our analysis is based on explicitly controlling the multiplier process arising from the interaction between the noise and the function evaluations on inputs. It allows for the interaction to be even polynomially heavy-tailed, which covers a significantly large class of heavy-tailed models beyond what is analyzed in the learning theory literature. We illustrate our results by deriving rates of convergence for the high-dimensional linear regression problem with dependent and heavy-tailed data.

The intention of writing this article is to show you all, " how Survival Analysis can be done using simple formulas of excel". Before I proceed further, let me share a formal definition of Survival analysis. "Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is time until an event occurs. The survivor function represents the probability that an individual survives from the time of origin to sometime beyond time, t." Keeping this definition in mind let us now proceed with our objective of implementing Survival Analysis using excel. I am considering a simple Case of the Manufacturing Unit where a bunch of old Machines having high chances of breakdown is chosen for Maintenance.

A common problem in the task of human-object interaction (HOI) detection is that numerous HOI classes have only a small number of labeled examples, resulting in training sets with a long-tailed distribution. The lack of positive labels can lead to low classification accuracy for these classes. Towards addressing this issue, we observe that there exist natural correlations and anti-correlations among human-object interactions. In this paper, we model the correlations as action co-occurrence matrices and present techniques to learn these priors and leverage them for more effective training, especially on rare classes. The efficacy of our approach is demonstrated experimentally, where the performance of our approach consistently improves over the state-of-the-art methods on both of the two leading HOI detection benchmark datasets, HICO-Det and V-COCO.

The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations without additional assumptions or by assuming a preconceived structure in the model, with the help of additional information about the system. In the second case, it is a question of adequately combining theory with observations and subsequently optimizing the mixture. In this work, we proposes the design of time-continuous models of dynamical systems as solutions of differential equations, from non-uniform sampled or noisy observations, using machine learning techniques. The performance of strategy is shown with both, several simulated data sets and experimental data from Hare-Lynx population and Coronavirus 2019 outbreack. Our results suggest that this approach to the modeling systems, can be an useful technique in the case of synthetic or experimental data.