We propose a method for causal inference using satellite image time series, in order to determine the treatment effects of interventions which impact climate change, such as deforestation. Simply put, the aim is to quantify the 'before versus after' effect of climate related human driven interventions, such as urbanization; as well as natural disasters, such as hurricanes and forest fires. As a concrete example, we focus on quantifying forest tree cover change/ deforestation due to human led causes. The proposed method involves the following steps. First, we uae computer vision and machine learning/deep learning techniques to detect and quantify forest tree coverage levels over time, at every time epoch. We then look at this time series to identify changepoints. Next, we estimate the expected (forest tree cover) values using a Bayesian structural causal model and projecting/forecasting the counterfactual. This is compared to the values actually observed post intervention, and the difference in the two values gives us the effect of the intervention (as compared to the non intervention scenario, i.e. what would have possibly happened without the intervention). As a specific use case, we analyze deforestation levels before and after the hyperinflation event (intervention) in Brazil (which ended in 1993-94), for the Amazon rainforest region, around Rondonia, Brazil. For this deforestation use case, using our causal inference framework can help causally attribute change/reduction in forest tree cover and increasing deforestation rates due to human activities at various points in time.

With the aim of building machine learning systems that incorporate standards of fairness and accountability, we explore explicit subgroup sample complexity bounds. The work is motivated by the observation that classifier predictions for real world datasets often demonstrate drastically different metrics, such as accuracy, when subdivided by specific sensitive variable subgroups. The reasons for these discrepancies are varied and not limited to the influence of mitigating variables, institutional bias, underlying population distributions as well as sampling bias. Among the numerous definitions of fairness that exist, we argue that at a minimum, principled ML practices should ensure that classification predictions are able to mirror the underlying sub-population distributions. However, as the number of sensitive variables increase, populations meeting at the intersectionality of these variables may simply not exist or may not be large enough to provide accurate samples for classification. In these increasingly likely scenarios, we make the case for human intervention and applying situational and individual definitions of fairness. In this paper we present lower bounds of subgroup sample complexity for metric-fair learning based on the theory of Probably Approximately Metric Fair Learning. We demonstrate that for a classifier to approach a definition of fairness in terms of specific sensitive variables, adequate subgroup population samples need to exist and the model dimensionality has to be aligned with subgroup population distributions. In cases where this is not feasible, we propose an approach using individual fairness definitions for achieving alignment. We look at two commonly explored UCI datasets under this lens and suggest human interventions for data collection for specific subgroups to achieve approximate individual fairness for linear hypotheses.

In graph neural networks (GNNs), pooling operators compute local summaries of input graphs to capture their global properties; in turn, they are fundamental operators for building deep GNNs that learn effective, hierarchical representations. In this work, we propose the Node Decimation Pooling (NDP), a pooling operator for GNNs that generates coarsened versions of a graph by leveraging on its topology only. During training, the GNN learns new representations for the vertices and fits them to a pyramid of coarsened graphs, which is computed in a pre-processing step. As theoretical contributions, we first demonstrate the equivalence between the MAXCUT partition and the node decimation procedure on which NDP is based. Then, we propose a procedure to sparsify the coarsened graphs for reducing the computational complexity in the GNN; we also demonstrate that it is possible to drop many edges without significantly altering the graph spectra of coarsened graphs. Experimental results show that NDP grants a significantly lower computational cost once compared to state-of-the-art graph pooling operators, while reaching, at the same time, competitive accuracy performance on a variety of graph classification tasks.

In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is often not sufficient. We propose and study calibration measures for multi-class classification that generalize existing measures such as the expected calibration error, the maximum calibration error, and the maximum mean calibration error. We propose and evaluate empirically different consistent and unbiased estimators for a specific class of measures based on matrix-valued kernels. Importantly, these estimators can be interpreted as test statistics associated with well-defined bounds and approximations of the p-value under the null hypothesis that the model is calibrated, significantly improving the interpretability of calibration measures, which otherwise lack any meaningful unit or scale.

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust formulation of PCA is derived based on the maximum correntropy criterion (MCC) so as to maximise the expected likelihood of Gaussian distributed reconstruction errors. In this way, the proposed solution reduces to a generalised power iteration, whereby: (i) robust estimates of the principal components are obtained even in the presence of outliers; (ii) the number of principal components need not be specified in advance; and (iii) the entire set of principal components can be obtained, unlike existing approaches. The advantages of the proposed maximum correntropy power iteration (MCPI) are demonstrated through an intuitive numerical example.

We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that oracle, our framework automatically generates a corresponding convex and smooth loss function. As we show, adding a projection as output layer provably makes the loss smaller. We identify the marginal polytope, the output space's convex hull, as the best convex set on which to project. However, because the projection onto the marginal polytope can sometimes be expensive to compute, we allow to use any convex superset instead, with potentially cheaper-to-compute projection. Since efficient projection algorithms are available for numerous convex sets, this allows us to construct loss functions for a variety of tasks. On the theoretical side, when combined with calibrated decoding, we prove that our loss functions can be used as a consistent surrogate for a (potentially non-convex) target loss function of interest. We demonstrate our losses on label ranking, ordinal regression and multilabel classification, confirming the improved accuracy enabled by projections.

Traditional event detection classifies a word or a phrase in a given sentence for a set of predefined event types. The limitation of such predefined set is that it prevents the adaptation of the event detection models to new event types. We study a novel formulation of event detection that describes types via several keywords to match the contexts in documents. This facilitates the operation of the models to new types. We introduce a novel feature-based attention mechanism for convolutional neural networks for event detection in the new formulation. Our extensive experiments demonstrate the benefits of the new formulation for new type extension for event detection as well as the proposed attention mechanism for this problem.

Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based on the assumption that all variables have been jointly measured in a single dataset. In many cases this assumption fails. Previous approaches to overcoming this shortcoming devised algorithms that returned all joint causal structures consistent with the conditional independence information contained in each individual dataset. But, as conditional independence tests only determine causal structure up to Markov equivalence, the number of consistent joint structures returned by these approaches can be quite large. The last decade has seen the development of elegant algorithms for discovering causal relations beyond conditional independence, which can distinguish among Markov equivalent structures. In this work we adapt and extend these so-called bivariate causal discovery algorithms to the problem of learning consistent causal structures from multiple datasets with overlapping variables belonging to the same generating process, providing a sound and complete algorithm that outperforms previous approaches on synthetic and real data.

The purpose of this paper is to introduced a new clustering methodology. This paper is divided into three parts. In the first part we have developed the axiomatic theory for the average silhouette width (ASW) index. There are different ways to investigate the quality and characteristics of clustering methods such as validation indices using simulations and real data experiments, model-based theory, and non-model-based theory known as the axiomatic theory. In this work we have not only taken the empirical approach of validation of clustering results through simulations, but also focus on the development of the axiomatic theory. In the second part we have presented a novel clustering methodology based on the optimization of the ASW index. We have considered the problem of estimation of number of clusters and finding clustering against this number simultaneously. Two algorithms are proposed. The proposed algorithms are evaluated against several partitioning and hierarchical clustering methods. An intensive empirical comparison of the different distance metrics on the various clustering methods is conducted. In the third part we have considered two application domains\textemdash novel single cell RNA sequencing datasets and rainfall data to cluster weather stations.

We propose a novel spectral convolutional neural network (CNN) model on graph structured data, namely Distributed Feedback-Looped Networks (DFNets). This model is incorporated with a robust class of spectral graph filters, called feedback-looped filters, to provide better localization on vertices, while still attaining fast convergence and linear memory requirements. Theoretically, feedback-looped filters can guarantee convergence w.r.t. a specified error bound, and be applied universally to any graph without knowing its structure. Furthermore, the propagation rule of this model can diversify features from the preceding layers to produce strong gradient flows. We have evaluated our model using two benchmark tasks: semi-supervised document classification on citation networks and semi-supervised entity classification on a knowledge graph. The experimental results show that our model considerably outperforms the state-of-the-art methods in both benchmark tasks over all datasets.