This work focuses on designing a pipeline for the prediction of bankruptcy. The presence of missing values, high dimensional data, and highly class-imbalance databases are the major challenges in the said task. A new method for missing data imputation with granular semantics has been introduced here. The merits of granular computing have been explored here to define this method. The missing values have been predicted using the feature semantics and reliable observations in a low-dimensional space, in the granular space. The granules are formed around every missing entry, considering a few of the highly correlated features and most reliable closest observations to preserve the relevance and reliability, the context, of the database against the missing entries. An intergranular prediction is then carried out for the imputation within those contextual granules. That is, the contextual granules enable a small relevant fraction of the huge database to be used for imputation and overcome the need to access the entire database repetitively for each missing value. This method is then implemented and tested for the prediction of bankruptcy with the Polish Bankruptcy dataset. It provides an efficient solution for big and high-dimensional datasets even with large imputation rates. Then an AI-driven pipeline for bankruptcy prediction has been designed using the proposed granular semantic-based data filling method followed by the solutions to the issues like high dimensional dataset and high class-imbalance in the dataset. The rest of the pipeline consists of feature selection with the random forest for reducing dimensionality, data balancing with SMOTE, and prediction with six different popular classifiers including deep NN. All methods defined here have been experimentally verified with suitable comparative studies and proven to be effective on all the data sets captured over the five years.

A structure-preserving kernel ridge regression method is presented that allows the recovery of potentially high-dimensional and nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form solution that yields excellent numerical performances that surpass other techniques proposed in the literature in this setup. From the methodological point of view, the paper extends kernel regression methods to problems in which loss functions involving linear functions of gradients are required and, in particular, a differential reproducing property and a Representer Theorem are proved in this context. The relation between the structure-preserving kernel estimator and the Gaussian posterior mean estimator is analyzed. A full error analysis is conducted that provides convergence rates using fixed and adaptive regularization parameters. The good performance of the proposed estimator is illustrated with various numerical experiments.

A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed approach aims to maximize the correlation between the so derived latent variables and is shown to be suitable for the prediction of multidimensional dependent data from multidimensional independent data, where for the estimation of the latent variables we introduce an algorithm based on Multilinear Singular Value Decomposition (MSVD) on a specially defined cross-covariance tensor. It is next shown that in this way we are also able to unify the existing Partial Least Squares (PLS) and N-way PLS regression algorithms within the same framework. Simulations on benchmark synthetic data confirm the advantages of the proposed approach, in terms of its predictive ability and robustness, especially for small sample sizes. The potential of the proposed technique is further illustrated on a real world task of the decoding of human intracranial electrocorticogram (ECoG) from a simultaneously recorded scalp electroencephalograph (EEG).

Brain-computer interfaces (BCIs) use brain signals to convey a user's intent. Some BCI approaches begin by decoding kinematic parameters of movements from brain signals, and then proceed to using these signals, in absence of movements, to allow a user to control an output. Recent results have shown that electrocorticographic (ECoG) recordings from the surface of the brain in humans can give information about kinematic parameters (e.g., hand velocity or finger flexion). The decoding approaches in these demonstrations usually employed classical classification/regression algorithms that derive a linear mapping between brain signals and outputs. However, they typically only incorporate little prior information about the target kinematic parameter.

An accurate model of patient survival time can help in the treatment and care of cancer patients. The common practice of providing survival time estimates based only on population averages for the site and stage of cancer ignores many important individual differences among patients. In this paper, we propose a local regression method for learning patient-specific survival time distribution based on patient attributes such as blood tests and clinical assessments. When tested on a cohort of more than 2000 cancer patients, our method gives survival time predictions that are much more accurate than popular survival analysis models such as the Cox and Aalen regression models. Our results also show that using patient-specific attributes can reduce the prediction error on survival time by as much as 20% when compared to using cancer site and stage only.

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a q-dimensional response, with a shared p-dimensional predictor variable. To control the complexity of the model, we employ a functional form of the Ky-Fan or nuclear norm, resulting in a set of function estimates that have low rank. Backfitting algorithms are derived and justified using a nonparametric form of the nuclear norm subdifferential. Oracle inequalities on excess risk are derived that exhibit the scaling behavior of the procedure in the high dimensional setting. The methods are illustrated on gene expression data.

This paper examines the possibility of a'reject option' in the context of least squares regression. It is shown that using rejection it is theoretically possible to learn'selective' regressors that can ǫ-pointwise track the best regressor in hindsight from the same hypothesis class, while rejecting only a bounded portion of the domain. Moreover, the rejected volume vanishes with the training set size, under certain conditions. We then develop efficient and exact implementation of these selective regressors for the case of linear regression. Empirical evaluation over a suite of real-world datasets corroborates the theoretical analysis and indicates that our selective regressors can provide substantial advantage by reducing estimation error.

We study the problem of diverse feature selection in linear regression: selecting a small subset of diverse features that can predict a given objective. Diversity is useful for several reasons such as interpretability, robustness to noise, etc. We propose several spectral regularizers that capture a notion of diversity of features and show that these are all submodular set functions. These regularizers, when added to the objective function for linear regression, result in approximately submodular functions, which can then be maximized by efficient greedy and local search algorithms, with provable guarantees.

In this paper, we present a Bayesian framework for multilabel classification using compressed sensing. The key idea in compressed sensing for multilabel classification is to first project the label vector to a lower dimensional space using a random transformation and then learn regression functions over these projections. Our approach considers both of these components in a single probabilistic model, thereby jointly optimizing over compression as well as learning tasks. We then derive an efficient variational inference scheme that provides joint posterior distribution over all the unobserved labels. The two key benefits of the model are that a) it can naturally handle datasets that have missing labels and b) it can also measure uncertainty in prediction. The uncertainty estimate provided by the model allows for active learning paradigms where an oracle provides information about labels that promise to be maximally informative for the prediction task. Our experiments show significant boost over prior methods in terms of prediction performance over benchmark datasets, both in the fully labeled and the missing labels case. Finally, we also highlight various useful active learning scenarios that are enabled by the probabilistic model.

We consider inference in a broad class of non-conjugate probabilistic models based on minimising the Kullback-Leibler divergence between the given target density and an approximating'variational' density. In particular, for generalised linear models we describe approximating densities formed from an affine transformation of independently distributed latent variables, this class including many well known densities as special cases. We show how all relevant quantities can be efficiently computed using the fast Fourier transform. This extends the known class of tractable variational approximations and enables the fitting for example of skew variational densities to the target density.