Related papers: Hierarchical correlation reconstruction with missi…
While we are usually focused on forecasting future values of time series, it is often valuable to additionally predict their entire probability distributions, e.g. to evaluate risk, Monte Carlo simulations. On example of time series of…
While we would like to predict exact values, available incomplete information is rarely sufficient - usually allowing only to predict conditional probability distributions. This article discusses hierarchical correlation reconstruction…
We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
It was recently proposed that neural networks could be used to approximate many-dimensional probability distributions that appear e.g. in lattice field theories or statistical mechanics. Subsequently they can be used as variational…
Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all…
We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sparse representation of the regression function in a…
This paper proposes multivariate copula models for hierarchical data. They account for two types of correlation: one is between variables measured on the same unit and the other is a correlation between units in the same cluster. This model…
The problem of missing data has been persistent for a long time and poses a major obstacle in machine learning and statistical data analysis. Past works in this field have tried using various data imputation techniques to fill in the…
In many complex applications, data heterogeneity and homogeneity exist simultaneously. Ignoring either one will result in incorrect statistical inference. In addition, coping with complex data that are non-Euclidean becomes more common. To…
In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of such rich and detailed physiological measurements calls for…
Differential network is an important tool to capture the changes of conditional correlations under two sample cases. In this paper, we introduce a fast iterative algorithm to recover the differential network for high-dimensional data. The…
In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In…
This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…
Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…
Detecting changes in high-dimensional vectors presents significant challenges, especially when the post-change distribution is unknown and time-varying. This paper introduces a novel robust algorithm for correlation change detection in…
Large collections of time series data are often organized into hierarchies with different levels of aggregation; examples include product and geographical groupings. Probabilistic coherent forecasting is tasked to produce forecasts…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
The relationship among three correlated variables could be very sophisticated, as a result, we may not be able to find their hidden causality and model their relationship explicitly. However, we still can make our best guess for possible…
Modern applications have made ubiquitous high-dimensional data, especially time-dependent data, with more and more complicated structures, and it also has become more frequent to encounter the scenario of hierarchical relationships among…