Once a classifier is estimated from the training data, it can be used to label new examples, and in many application domains, such as character recognition, text classification and oth- ers, this constitutes the final goal of the learning stage. The statistical learning algorithms are also used in scientific studies to detect and analyze differences between the two classes when the correct answer'' is unknown, and the information we have on the differences is represented implicitly by the training set. Example applications include morphologi- cal analysis of anatomical organs (comparing organ shape in patients vs. normal controls), molecular design (identifying complex molecules that satisfy certain requirements), etc. In such applications, interpretation of the resulting classifier in terms of the original feature vectors can provide an insight into the nature of the differences detected by the learning algorithm and is therefore a crucial step in the analysis. Furthermore, we would argue that studying the spatial structure of the data captured by the classification function is important in any application, as it leads to a better understanding of the data and can potentially help in improving the technique.

The underspecification of most machine learning pipelines means that we cannot rely solely on validation performance to assess the robustness of deep learning systems to naturally occurring distribution shifts. Instead, making sure that a neural network can generalize across a large number of different situations requires to understand the specific way in which it solves a task. In this work, we propose to study this problem from a geometric perspective with the aim to understand two key characteristics of neural network solutions in underspecified settings: how is the geometry of the learned function related to the data representation? And, are deep networks always biased towards simpler solutions, as conjectured in recent literature? We show that the way neural networks handle the underspecification of these problems is highly dependent on the data representation, affecting both the geometry and the complexity of the learned predictors. Our results highlight that understanding the architectural inductive bias in deep learning is fundamental to address the fairness, robustness, and generalization of these systems.

Heterogeneous domain adaptation (HDA) aims to facilitate the learning task in a target domain by borrowing knowledge from a heterogeneous source domain. In this paper, we propose a Soft Transfer Network (STN), which jointly learns a domain-shared classifier and a domain-invariant subspace in an end-to-end manner, for addressing the HDA problem. The proposed STN not only aligns the discriminative directions of domains but also matches both the marginal and conditional distributions across domains. To circumvent negative transfer, STN aligns the conditional distributions by using the soft-label strategy of unlabeled target data, which prevents the hard assignment of each unlabeled target data to only one category that may be incorrect. Further, STN introduces an adaptive coefficient to gradually increase the importance of the soft-labels since they will become more and more accurate as the number of iterations increases. We perform experiments on the transfer tasks of image-to-image, text-to-image, and text-to-text. Experimental results testify that the STN significantly outperforms several state-of-the-art approaches.

We propose a formulation of visual localization that does not require construction of explicit maps in the form of point clouds or voxels. The goal is to learn an implicit representation of the environment at a higher, more abstract level, for instance that of objects. To study this approach we consider procedurally generated Minecraft worlds, for which we can generate visually rich images along with camera pose coordinates. We first show that Generative Query Networks (GQNs) enhanced with a novel attention mechanism can capture the visual structure of 3D scenes in Minecraft, as evidenced by their samples. We then apply the models to the localization problem, investigating both generative and discriminative approaches, and compare the different ways in which they each capture task uncertainty. Our results show that models with implicit mapping are able to capture the underlying 3D structure of visually complex scenes, and use this to accurately localize new observations, paving the way towards future applications in sequential localization. Supplementary video available at https://youtu.be/iHEXX5wXbCI.

This thesis derives, tests and applies two linear projection algorithms for machine learning under non-stationarity. The first finds a direction in a linear space upon which a data set is maximally non-stationary. The second aims to robustify two-way classification against non-stationarity. The algorithm is tested on a key application scenario, namely Brain Computer Interfacing.

In many scientific and engineering applications, detecting and understanding differences between two groups of examples can be reduced to a classical problem of training a classifier for labeling new examples while making as few mistakes as possible. In the traditional classification setting, the resulting classifier is rarely analyzed in terms of the properties of the input data captured by the discriminative model. However, such analysis is crucial if we want to understand and visualize the detected differences. We propose an approach to interpretation of the statistical model in the original feature space that allows us to argue about the model in terms of the relevant changes to the input vectors. For each point in the input space, we define a discriminative direction to be the direction that moves the point towards the other class while introducing as little irrelevant change as possible with respect to the classifier function. We derive the discriminative direction for kernel-based classifiers, demonstrate the technique on several examples and briefly discuss its use in the statistical shape analysis, an application that originally motivated this work.

In many scientific and engineering applications, detecting and understanding differences between two groups of examples can be reduced to a classical problem of training a classifier for labeling new examples while making as few mistakes as possible. In the traditional classification setting, the resulting classifier is rarely analyzed in terms of the properties of the input data captured by the discriminative model. However, such analysis is crucial if we want to understand and visualize the detected differences. We propose an approach to interpretation of the statistical model in the original feature space that allows us to argue about the model in terms of the relevant changes to the input vectors. For each point in the input space, we define a discriminative direction to be the direction that moves the point towards the other class while introducing as little irrelevant change as possible with respect to the classifier function. We derive the discriminative direction for kernel-based classifiers, demonstrate the technique on several examples and briefly discuss its use in the statistical shape analysis, an application that originally motivated this work.

In many scientific and engineering applications, detecting and understanding differencesbetween two groups of examples can be reduced to a classical problem of training a classifier for labeling new examples while making as few mistakes as possible. In the traditional classification setting,the resulting classifier is rarely analyzed in terms of the properties of the input data captured by the discriminative model. However, suchanalysis is crucial if we want to understand and visualize the detected differences. We propose an approach to interpretation of the statistical modelin the original feature space that allows us to argue about the model in terms of the relevant changes to the input vectors. For each point in the input space, we define a discriminative direction to be the direction that moves the point towards the other class while introducing as little irrelevant change as possible with respect to the classifier function. Wederive the discriminative direction for kernel-based classifiers, demonstrate the technique on several examples and briefly discuss its use in the statistical shape analysis, an application that originally motivated this work.