In several financial applications, it is necessary to understand risk sensitivity while maximizing the returns. Several risk measures have been studied in the literature, e.g., mean-variance, Value at Risk (VaR), Conditional Value at Risk (CVaR), distorted risk measure, and prospect theory. In [2], the authors consider four properties as desirable for a risk measure, namely positive homogeneity, translation invariance, sub-additivity, and monotonicity. They define a risk measure as being coherent if it possesses the aforementioned properties. In a related development, in[19], the authors chose to relax the sub-additivity and positive homogeneity requirements of a coherent risk measure, and instead impose a convexity condition on the underlying risk measure.

Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue by assessing DNNs' ability to estimate conditional probabilities and propose a framework for systematic uncertainty characterization. Denoting the input sample as x and the category as y, the classification task of assigning a category y to a given input x can be reduced to the task of estimating the conditional probabilities p(y|x), as approximated by the DNN at its last layer using the softmax function. Since softmax yields a vector whose elements all fall in the interval (0, 1) and sum to 1, it suggests a probabilistic interpretation to the DNN's outcome. Using synthetic and real-world datasets, we look into the impact of various factors, e.g., probability density f(x) and inter-categorical sparsity, on the precision of DNNs' estimations of p(y|x), and find that the likelihood probability density and the inter-categorical sparsity have greater impacts than the prior probability to DNNs' classification uncertainty.

A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label distributions remain the same. Despite the prevalence of covariate shift in real-world applications, a theoretical understanding in the context of modern machine learning has remained lacking. In this work, we examine the exact high-dimensional asymptotics of random feature regression under covariate shift and present a precise characterization of the limiting test error, bias, and variance in this setting. Our results motivate a natural partial order over covariate shifts that provides a sufficient condition for determining when the shift will harm (or even help) test performance. We find that overparameterized models exhibit enhanced robustness to covariate shift, providing one of the first theoretical explanations for this intriguing phenomenon. Additionally, our analysis reveals an exact linear relationship between in-distribution and out-of-distribution generalization performance, offering an explanation for this surprising recent empirical observation.

Graph convolutional network (GCN) is a powerful model studied broadly in various graph structural data learning tasks. However, to mitigate the over-smoothing phenomenon, and deal with heterogeneous graph structural data, the design of GCN model remains a crucial issue to be investigated. In this paper, we propose a novel GCN called SStaGCN (Simplified stacking based GCN) by utilizing the ideas of stacking and aggregation, which is an adaptive general framework for tackling heterogeneous graph data. Specifically, we first use the base models of stacking to extract the node features of a graph. Subsequently, aggregation methods such as mean, attention and voting techniques are employed to further enhance the ability of node features extraction. Thereafter, the node features are considered as inputs and fed into vanilla GCN model. Furthermore, theoretical generalization bound analysis of the proposed model is explicitly given. Extensive experiments on $3$ public citation networks and another $3$ heterogeneous tabular data demonstrate the effectiveness and efficiency of the proposed approach over state-of-the-art GCNs. Notably, the proposed SStaGCN can efficiently mitigate the over-smoothing problem of GCN.

Predictors map individual instances in a population to the interval $[0,1]$. For a collection $\mathcal C$ of subsets of a population, a predictor is multi-calibrated with respect to $\mathcal C$ if it is simultaneously calibrated on each set in $\mathcal C$. We initiate the study of the construction of scaffolding sets, a small collection $\mathcal S$ of sets with the property that multi-calibration with respect to $\mathcal S$ ensures correctness, and not just calibration, of the predictor. Our approach is inspired by the folk wisdom that the intermediate layers of a neural net learn a highly structured and useful data representation.

The MineRL competition is designed for the development of reinforcement learning and imitation learning algorithms that can efficiently leverage human demonstrations to drastically reduce the number of environment interactions needed to solve the complex ObtainDiamond task with sparse rewards. To address the challenge, in this paper, we present SEIHAI, a Sample-efficient Hierarchical AI, that fully takes advantage of the human demonstrations and the task structure. Specifically, we split the task into several sequentially dependent subtasks, and train a suitable agent for each subtask using reinforcement learning and imitation learning. We further design a scheduler to select different agents for different subtasks automatically. SEIHAI takes the first place in the preliminary and final of the NeurIPS-2020 MineRL competition.

Understanding 3D scenes is a critical prerequisite for autonomous agents. Recently, LiDAR and other sensors have made large amounts of data available in the form of temporal sequences of point cloud frames. In this work, we propose a novel problem -- sequential scene flow estimation (SSFE) -- that aims to predict 3D scene flow for all pairs of point clouds in a given sequence. This is unlike the previously studied problem of scene flow estimation which focuses on two frames. We introduce the SPCM-Net architecture, which solves this problem by computing multi-scale spatiotemporal correlations between neighboring point clouds and then aggregating the correlation across time with an order-invariant recurrent unit. Our experimental evaluation confirms that recurrent processing of point cloud sequences results in significantly better SSFE compared to using only two frames. Additionally, we demonstrate that this approach can be effectively modified for sequential point cloud forecasting (SPF), a related problem that demands forecasting future point cloud frames. Our experimental results are evaluated using a new benchmark for both SSFE and SPF consisting of synthetic and real datasets. Previously, datasets for scene flow estimation have been limited to two frames. We provide non-trivial extensions to these datasets for multi-frame estimation and prediction. Due to the difficulty of obtaining ground truth motion for real-world datasets, we use self-supervised training and evaluation metrics. We believe that this benchmark will be pivotal to future research in this area. All code for benchmark and models will be made accessible.

The four essential chambers of one's heart that lie in the thoracic cavity are crucial for one's survival, yet ironically prove to be the most vulnerable. Cardiovascular disease (CVD) also commonly referred to as heart disease has steadily grown to the leading cause of death amongst humans over the past few decades. Taking this concerning statistic into consideration, it is evident that patients suffering from CVDs need a quick and correct diagnosis in order to facilitate early treatment to lessen the chances of fatality. This paper attempts to utilize the data provided to train classification models such as Logistic Regression, K Nearest Neighbors, Support Vector Machine, Decision Tree, Gaussian Naive Bayes, Random Forest, and Multi-Layer Perceptron (Artificial Neural Network) and eventually using a soft voting ensemble technique in order to attain as many correct diagnoses as possible.

Time series data generation has drawn increasing attention in recent years. Several generative adversarial network (GAN) based methods have been proposed to tackle the problem usually with the assumption that the targeted time series data are well-formatted and complete. However, real-world time series (RTS) data are far away from this utopia, e.g., long sequences with variable lengths and informative missing data raise intractable challenges for designing powerful generation algorithms. In this paper, we propose a novel generative framework for RTS data - RTSGAN to tackle the aforementioned challenges. RTSGAN first learns an encoder-decoder module which provides a mapping between a time series instance and a fixed-dimension latent vector and then learns a generation module to generate vectors in the same latent space. By combining the generator and the decoder, RTSGAN is able to generate RTS which respect the original feature distributions and the temporal dynamics. To generate time series with missing values, we further equip RTSGAN with an observation embedding layer and a decide-and-generate decoder to better utilize the informative missing patterns. Experiments on the four RTS datasets show that the proposed framework outperforms the previous generation methods in terms of synthetic data utility for downstream classification and prediction tasks.

Gene expression datasets are usually of high dimensionality and therefore require efficient and effective methods for identifying the relative importance of their attributes. Due to the huge size of the search space of the possible solutions, the attribute subset evaluation feature selection methods tend to be not applicable, so in these scenarios feature ranking methods are used. Most of the feature ranking methods described in the literature are univariate methods, so they do not detect interactions between factors. In this paper we propose two new multivariate feature ranking methods based on pairwise correlation and pairwise consistency, which we have applied in three gene expression classification problems. We statistically prove that the proposed methods outperform the state of the art feature ranking methods Clustering Variation, Chi Squared, Correlation, Information Gain, ReliefF and Significance, as well as feature selection methods of attribute subset evaluation based on correlation and consistency with multi-objective evolutionary search strategy.