Learning, compression, and leakage: Minimising classification error via meta-universal compression principles

Learning and compression are driven by the common aim of identifying and exploiting statistical regularities in data, which opens the door for fertile collaboration between these areas. A promising group of compression techniques for learning scenarios is normalised maximum likelihood (NML) coding, which provides strong guarantees for compression of small datasets - in contrast with more popular estimators whose guarantees hold only in the asymptotic limit. Here we consider a NML-based decision strategy for supervised classification problems, and show that it attains heuristic PAC learning when applied to a wide variety of models. Furthermore, we show that the misclassification rate of our method is upper bounded by the maximal leakage, a recently proposed metric to quantify the potential of data leakage in privacy-sensitive scenarios.

Graph-based image representation learning

Renata Khasanova

Though deep learning (DL) algorithms are very powerful for image processing tasks, they generally require a lot of data to reach their full potential. Furthermore, there is no straightforward way to impose various properties, given by the prior knowledge about the target task, on the features extracted by a DL model. Therefore, in this thesis we propose several techniques that rely on the power of graph representations to embed prior knowledge inside the learning process. This allows to reduce the solution space and leads to faster optimization convergence and higher accuracy in the representation learning. In our first work, inspired by the ability of a human to correctly classify rotated, shifted or flipped objects, we propose an algorithm that permits to inherently encode invariance to isometric transformations of objects in an image. Our DL architecture is based on graph representations and consists of three novel layers, which we refer to as graph convolutional, dynamic pooling and statistical layers. Our experiments on the image classification tasks show that our network correctly recognizes isometrically transformed objects even though such types of transformation are not seen by the network at training time. Standard DL techniques are typically not able to succeed in solving such a problem without extensive data augmentation. Then, we propose to exploit the properties of graph-based approaches to efficiently process images with various types of projective geometry. In particular, we are interested in increasingly popular omnidirectional cameras, which have a 360 degree field of view. Despite their effectiveness, such cameras create images with specific geometric properties, which require special techniques for efficient processing. We propose an efficient way of adjusting the weights of the graph edges to adapt the filter responses to the geometric image properties introduced by omnidirectional cameras. Our experiments prove that using the proposed graph with properly adjusted edge weights permits to reach better performance as compared to using regular grid graph with equal weights. Finally, the approach described above relies on the isotropic filters, which work well within our transformation invariant architecture for image classification. However, for other problems (e.g. image compression) or even when used without dynamic pooling and statistical layers that are defined within the proposed architecture, these filters are unable to efficiently encode the information about the object. Thus, we introduce a different technique based on anisotropic filters that adapt their shape and size according to the omnidirectional image geometry. The main advantage of this approach compared to the previous one is the ability to encode the orientation of an image pattern, which is important for various tasks such as image compression. Our experiments show that our approach adapts to different image projective geometries and achieves state-of-the-art performance on image classification and compression tasks. Overall we propose several methods, which combine the power of DL and graph signal processing towards incorporating prior information about the target task inside the optimization procedure. We hope that the research efforts presented in this thesis will help the development of efficient DL algorithms that can use various types of prior knowledge to make them efficient even when the available training data is scarce.

EPFL2019

Prior knowledge in Kernel methods

Alexei Pozdnoukhov

Machine Learning is a modern and actively developing field of computer science, devoted to extracting and estimating dependencies from empirical data. It combines such fields as statistics, optimization theory and artificial intelligence. In practical tasks, the general aim of Machine Learning is to construct algorithms able to generalize and predict in previously unseen situations based on some set of examples. Given some finite information, Machine Learning provides ways to exract knowledge, describe, explain and predict from data. Kernel Methods are one of the most successful branches of Machine Learning. They allow applying linear algorithms with well-founded properties such as generalization ability, to non-linear real-life problems. Support Vector Machine is a well-known example of a kernel method, which has found a wide range of applications in data analysis nowadays. In many practical applications, some additional prior knowledge is often available. This can be the knowledge about the data domain, invariant transformations, inner geometrical structures in data, some properties of the underlying process, etc. If used smartly, this information can provide significant improvement to any data processing algorithm. Thus, it is important to develop methods for incorporating prior knowledge into data-dependent models. The main objective of this thesis is to investigate approaches towards learning with kernel methods using prior knowledge. Invariant learning with kernel methods is considered in more details. In the first part of the thesis, kernels are developed which incorporate prior knowledge on invariant transformations. They apply when the desired transformation produce an object around every example, assuming that all points in the given object share the same class. Different types of objects, including hard geometrical objects and distributions are considered. These kernels were then applied for images classification with Support Vector Machines. Next, algorithms which specifically include prior knowledge are considered. An algorithm which linearly classifies distributions by their domain was developed. It is constructed such that it allows to apply kernels to solve non-linear tasks. Thus, it combines the discriminative power of support vector machines and the well-developed framework of generative models. It can be applied to a number of real-life tasks which include data represented as distributions. In the last part of the thesis, the use of unlabelled data as a source of prior knowledge is considered. The technique of modelling the unlabelled data with a graph is taken as a baseline from semi-supervised manifold learning. For classification problems, we use this apporach for building graph models of invariant manifolds. For regression problems, we use unlabelled data to take into account the inner geometry of the input space. To conclude, in this thesis we developed a number of approaches for incorporating some prior knowledge into kernel methods. We proposed invariant kernels for existing algorithms, developed new algorithms and adapted a technique taken from semi-supervised learning for invariant learning. In all these cases, links with related state-of-the-art approaches were investigated. Several illustrative experiments were carried out on real data on optical character recognition, face image classification, brain-computer interfaces, and a number of benchmark and synthetic datasets.

EPFL2006

Learning the structure of image collections with latent aspect models

Florent Monay Michaud

The approach to indexing an image collection depends on the type of data to organize. Satellite images are likely to be searched with latitude and longitude coordinates, medical images are often searched with an image example that serves as a visual query, and personal image collections are generally browsed by event. A more general retrieval scenario is based on the use of textual keywords to search for images containing a specific object, or representing a given scene type. This requires the manual annotation of each image in the collection to allow for the retrieval of relevant visual information based on a text query. This time-consuming and subjective process is the current price to pay for a reliable and convenient text-based image search. This dissertation investigates the use of probabilistic models to assist the automatic organization of image collections, attempting to link the visual content of digital images with a potential textual description. Relying on robust, patch-based image representations that have proven to capture a variety of visual content, our work proposes to model images as mixtures of latent aspects. These latent aspects are defined by multinomial distributions that capture patch co-occurrence information observed in the collection. An image is not represented by the direct count of its constituting elements, but as a mixture of latent aspects that can be estimated with principled, generative unsupervised learning methods. An aspect-based image representation therefore incorporates contextual information from the whole collection that can be exploited. This emerging concept is explored for several fundamental tasks related to image retrieval – namely classification, clustering, segmentation, and annotation – in what represents one of the first coherent and comprehensive study of the subject. We first investigate the possibility of classifying images based on their estimated aspect mixture weights, interpreting latent aspect modeling as an unsupervised feature extraction process. Several image categorization tasks are considered, where images are classified based on the present objects or according to their global scene type. We demonstrate that the concept of latent aspects allows to take advantage of non-labeled data to infer a robust image representation that achieves a higher classification performance than the original patch-based representation. Secondly, further exploring the concept, we show that aspects can correspond to an interesting soft clustering of an image collection that can serve as a browsing structure. Images can be ranked given an aspect, illustrating the corresponding co-occurrence context visually. In the third place, we derive a principled method that relies on latent aspects to classify image patches into different categories. This produces an image segmentation based on the resulting spatial class-densities. We finally propose to model images and their caption with a single aspect model, merging the co-occurrence contexts of the visual and the textual modalities in different ways. Once a model has been learned, the distribution of words given an unseen image is inferred based on its visual representation, and serves as textual indexing. Overall, we demonstrate with extensive experiments that the co-occurrence context captured by latent aspects is suitable for the above mentioned tasks, making it a promising approach for multimedia indexing.

EPFL2007