Optimization methods for collaborative learning

A traditional machine learning pipeline involves collecting massive amounts of data centrally on a server and training models to fit the data. However, increasing concerns about the privacy and security of user's data, combined with the sheer growth in the data sizes has incentivized looking beyond such traditional centralized approaches. Collaborative learning (which encompasses distributed, federated, and decentralized learning) proposes instead for a network of data holders to collaborate together to train models without transmitting any data. This new paradigm minimizes data exposure, but inherently faces some fundamental challenges. In this thesis, we bring to bear the framework of stochastic optimization to formalize and develop new algorithms for these challenges. This serves not only to develop novel solutions, but also to test the utility of the optimization lens in modern deep learning.We study three fundamental problems. Firstly, collaborative training replaces a one-time transmission of raw data with repeated rounds of communicating partially trained models. However, this quickly runs against bandwidth constraints when dealing with large models. We propose to solve this bandwidth constraint using compressed communication. Next, collaborative training leverages the computation power of the data holders directly. However, this is not as reliable as using a data center with only a subset of them available at any given time. Thus, we require new algorithms which can efficiently utilize unreliable local computation of the data holders. Finally, collaborative training allows any data holder to participate in the training process, without being able to inspect their data or local computation. This may potentially open the system to malicious or faulty agents who seek to derail the training. We develop algorithms with Byzantine robustness which are guaranteed to be resilient to such attackers.

Motion models for robust 3D human body tracking

Raquel Urtasun

In this work, we propose new ways to learn pose and motion priors models and show that they can be used to increase the performance of 3D body tracking algorithms, resulting in very realistic motions under very challenging conditions. We first explored an approach to 3D people tracking that combines learned motion models and deterministic optimization. The tracking problem is formulated as the minimization of a differentiable criterion whose differential structure is rich enough for optimization to be accomplished via hill-climbing. This avoids the computational expense of Monte Carlo methods, while yielding very good results under challenging conditions. To demonstrate the generality of the approach we show that we can learn and track cyclic motions such as walking and running, as well as acyclic motions such as a golf swing. We also show results from both monocular and multi-camera tracking. Finally, we provide results with a motion model learned from multiple activities, and show how these models can be used for recognition and motion generation. The major limitation of these linear motion models is that they required many noiseless, segmented and time warped examples to create a complete database with good generalization properties. We therefore investigated more complex non-linear statistical techniques. We advocate the use of Scaled Gaussian Process Latent Variable Models (SGPLVM) to learn prior models of 3D human pose. The SGPLVM simultaneously optimizes a low-dimensional embedding of the high-dimensional pose data and a density function that both gives higher probability to points close to training data and provides a nonlinear probabilistic mapping from the low-dimensional latent space to the full-dimensional pose space. The SGPLVM is a natural choice when only small amounts of training data are available. We demonstrate our approach with two distinct motions, golfing and walking. We show that the SGPLVM sufficiently constrains the problem such that tracking can be accomplished with straightforward deterministic optimization. However, in the presence of very noisy or missing data, for example due to occlusions, the simplistic second order Markov model we use is not realistic enough to sufficiently constrain the algorithm. Moreover, when learning models that contain stylistic diversity, from different people or from the same person performing an activity multiple times, the SGPLVM results in models whose latent trajectories are not smooth, and are therefore not suited for hill climbing tracking. Finally, we present a more powerfull approach based on the Gaussian Process Dynamical Models (GPDMs) that combines the strengths of the two previous ones. We advocate the use of GPDMs for learning human pose and motion priors. A GPDM provides a low-dimensional embedding of human motion data, with a density function that gives higher probability to poses and motions close to the training data. With Bayesian model averaging a GPDM can be learned from relatively small amounts of data, and it generalizes gracefully to motions outside the training set. Here we modify the GPDM to permit learning from motions with significant stylistic variation. The resulting priors are effective for tracking a range of human walking styles, despite weak and noisy image measurements and significant occlusions.

EPFL2006

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

Prior Knowledge in Kernel Methods

Alexei Pozdnoukhov

École Polytechnique Fédérale de Lausanne2006

Prior knowledge in Kernel methods

Alexei Pozdnoukhov

EPFL2006

Prior Knowledge in Kernel Methods

Alexei Pozdnoukhov

École Polytechnique Fédérale de Lausanne2006

Motion models for robust 3D human body tracking

Raquel Urtasun

EPFL2006