arXiv subjects

Marius Kloft

Publications and source records attributed to Marius Kloft.

At least 73 records · Page 4Linked to original sources

arXiv2020

Deep Semi-Supervised Anomaly Detection

Deep approaches to anomaly detection have recently shown promising results over shallow methods on large and complex datasets. Typically anomaly detection is treated as an unsupervised learning problem. In practice however, one may have---in addition to a large set of unlabeled samples---access to a small pool of labeled samples, e.g. a subset verified by some domain expert as being normal or anomalous. Semi-supervised approaches to anomaly detection aim to utilize such labeled samples, but most proposed methods are limited to merely including labeled normal samples. Only a few methods take advantage of labeled anomalies, with existing deep approaches being domain-specific. In this work we present Deep SAD, an end-to-end deep methodology for general semi-supervised anomaly detection. We further introduce an information-theoretic framework for deep anomaly detection based on the idea that the entropy of the latent distribution for normal data should be lower than the entropy of the anomalous distribution, which can serve as a theoretical interpretation for our method. In extensive experiments on MNIST, Fashion-MNIST, and CIFAR-10, along with other anomaly detection benchmark datasets, we demonstrate that our method is on par or outperforms shallow, hybrid, and deep competitors, yielding appreciable performance improvements even when provided with only little labeled data.

cs.LG↗

arXiv2020

Machine Learning in Thermodynamics: Prediction of Activity Coefficients by Matrix Completion

Activity coefficients, which are a measure of the non-ideality of liquid mixtures, are a key property in chemical engineering with relevance to modeling chemical and phase equilibria as well as transport processes. Although experimental data on thousands of binary mixtures are available, prediction methods are needed to calculate the activity coefficients in many relevant mixtures that have not been explored to-date. In this report, we propose a probabilistic matrix factorization model for predicting the activity coefficients in arbitrary binary mixtures. Although no physical descriptors for the considered components were used, our method outperforms the state-of-the-art method that has been refined over three decades while requiring much less training effort. This opens perspectives to novel methods for predicting physico-chemical properties of binary mixtures with the potential to revolutionize modeling and simulation in chemical engineering.

physics.chem-ph↗

arXiv2019

Analyzing the Variance of Policy Gradient Estimators for the Linear-Quadratic Regulator

We study the variance of the REINFORCE policy gradient estimator in environments with continuous state and action spaces, linear dynamics, quadratic cost, and Gaussian noise. These simple environments allow us to derive bounds on the estimator variance in terms of the environment and noise parameters. We compare the predictions of our bounds to the empirical variance in simulation experiments.

cs.LG↗

arXiv2018

Efficient Gaussian Process Classification Using Polya-Gamma Data Augmentation

We propose a scalable stochastic variational approach to GP classification building on Polya-Gamma data augmentation and inducing points. Unlike former approaches, we obtain closed-form updates based on natural gradients that lead to efficient optimization. We evaluate the algorithm on real-world datasets containing up to 11 million data points and demonstrate that it is up to two orders of magnitude faster than the state-of-the-art while being competitive in terms of prediction performance.

stat.ML↗

arXiv2018

Scalable Generalized Dynamic Topic Models

Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.

stat.ML↗

arXiv2017

Data-dependent Generalization Bounds for Multi-class Classification

In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for empirical multi-class risk minimization algorithms using an arbitrary norm as regularizer. Key to our analysis are new structural results for multi-class Gaussian complexities and empirical $\ell_\infty$-norm covering numbers, which exploit the Lipschitz continuity of the loss function with respect to the $\ell_2$- and $\ell_\infty$-norm, respectively. We establish data-dependent error bounds in terms of complexities of a linear function class defined on a finite set induced by training examples, for which we show tight lower and upper bounds. We apply the results to several prominent multi-class learning machines, exhibiting a tighter dependency on the number of classes than the state of the art. For instance, for the multi-class SVM by Crammer and Singer (2002), we obtain a data-dependent bound with a logarithmic dependency which significantly improves the previous square-root dependency. Experimental results are reported to verify the effectiveness of our theoretical findings.

cs.LG↗

arXiv2017

Bayesian Nonlinear Support Vector Machines for Big Data

We propose a fast inference method for Bayesian nonlinear support vector machines that leverages stochastic variational inference and inducing points. Our experiments show that the proposed method is faster than competing Bayesian approaches and scales easily to millions of data points. It provides additional features over frequentist competitors such as accurate predictive uncertainty estimates and automatic hyperparameter search.

stat.ML↗

arXiv2017

Sparse Probit Linear Mixed Model

Linear Mixed Models (LMMs) are important tools in statistical genetics. When used for feature selection, they allow to find a sparse set of genetic traits that best predict a continuous phenotype of interest, while simultaneously correcting for various confounding factors such as age, ethnicity and population structure. Formulated as models for linear regression, LMMs have been restricted to continuous phenotypes. We introduce the Sparse Probit Linear Mixed Model (Probit-LMM), where we generalize the LMM modeling paradigm to binary phenotypes. As a technical challenge, the model no longer possesses a closed-form likelihood function. In this paper, we present a scalable approximate inference algorithm that lets us fit the model to high-dimensional data sets. We show on three real-world examples from different domains that in the setup of binary labels, our algorithm leads to better prediction accuracies and also selects features which show less correlation with the confounding factors.

stat.ML↗

arXiv2017

Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learning

We show a Talagrand-type concentration inequality for Multi-Task Learning (MTL), using which we establish sharp excess risk bounds for MTL in terms of distribution- and data-dependent versions of the Local Rademacher Complexity (LRC). We also give a new bound on the LRC for norm regularized as well as strongly convex hypothesis classes, which applies not only to MTL but also to the standard i.i.d. setting. Combining both results, one can now easily derive fast-rate bounds on the excess risk for many prominent MTL methods, including---as we demonstrate---Schatten-norm, group-norm, and graph-regularized MTL. The derived bounds reflect a relationship akeen to a conservation law of asymptotic convergence rates. This very relationship allows for trading off slower rates w.r.t. the number of tasks for faster rates with respect to the number of available samples per task, when compared to the rates obtained via a traditional, global Rademacher analysis.

cs.LG↗

arXiv2016

Distributed Optimization of Multi-Class SVMs

Training of one-vs.-rest SVMs can be parallelized over the number of classes in a straight forward way. Given enough computational resources, one-vs.-rest SVMs can thus be trained on data involving a large number of classes. The same cannot be stated, however, for the so-called all-in-one SVMs, which require solving a quadratic program of size quadratically in the number of classes. We develop distributed algorithms for two all-in-one SVM formulations (Lee et al. and Weston and Watkins) that parallelize the computation evenly over the number of classes. This allows us to compare these models to one-vs.-rest SVMs on unprecedented scale. The results indicate superior accuracy on text classification data.

stat.ML↗

arXiv2016

Feature Importance Measure for Non-linear Learning Algorithms

Complex problems may require sophisticated, non-linear learning methods such as kernel machines or deep neural networks to achieve state of the art prediction accuracies. However, high prediction accuracies are not the only objective to consider when solving problems using machine learning. Instead, particular scientific applications require some explanation of the learned prediction function. Unfortunately, most methods do not come with out of the box straight forward interpretation. Even linear prediction functions are not straight forward to explain if features exhibit complex correlation structure. In this paper, we propose the Measure of Feature Importance (MFI). MFI is general and can be applied to any arbitrary learning machine (including kernel machines and deep learning). MFI is intrinsically non-linear and can detect features that by itself are inconspicuous and only impact the prediction function through their interaction with other features. Lastly, MFI can be used for both --- model-based feature importance and instance-based feature importance (i.e, measuring the importance of a feature for a particular data point).

cs.AI↗

arXiv2016

Localized Multiple Kernel Learning---A Convex Approach

We propose a localized approach to multiple kernel learning that can be formulated as a convex optimization problem over a given cluster structure. For which we obtain generalization error guarantees and derive an optimization algorithm based on the Fenchel dual representation. Experiments on real-world datasets from the application domains of computational biology and computer vision show that convex localized multiple kernel learning can achieve higher prediction accuracies than its global and non-convex local counterparts.

cs.LG↗

arXiv2015

Framework for Multi-task Multiple Kernel Learning and Applications in Genome Analysis

We present a general regularization-based framework for Multi-task learning (MTL), in which the similarity between tasks can be learned or refined using $\ell_p$-norm Multiple Kernel learning (MKL). Based on this very general formulation (including a general loss function), we derive the corresponding dual formulation using Fenchel duality applied to Hermitian matrices. We show that numerous established MTL methods can be derived as special cases from both, the primal and dual of our formulation. Furthermore, we derive a modern dual-coordinate descend optimization strategy for the hinge-loss variant of our formulation and provide convergence bounds for our algorithm. As a special case, we implement in C++ a fast LibLinear-style solver for $\ell_p$-norm MKL. In the experimental section, we analyze various aspects of our algorithm such as predictive performance and ability to reconstruct task relationships on biologically inspired synthetic data, where we have full control over the underlying ground truth. We also experiment on a new dataset from the domain of computational biology that we collected for the purpose of this paper. It concerns the prediction of transcription start sites (TSS) over nine organisms, which is a crucial task in gene finding. Our solvers including all discussed special cases are made available as open-source software as part of the SHOGUN machine learning toolbox (available at \url{http://shogun.ml}).

stat.ML↗

arXiv2015

Multi-class SVMs: From Tighter Data-Dependent Generalization Bounds to Novel Algorithms

This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially improving the state-of-the-art linear dependence in the existing data-dependent generalization analysis. The theoretical analysis motivates us to introduce a new multi-class classification machine based on $\ell_p$-norm regularization, where the parameter $p$ controls the complexity of the corresponding bounds. We derive an efficient optimization algorithm based on Fenchel duality theory. Benchmarks on several real-world datasets show that the proposed algorithm can achieve significant accuracy gains over the state of the art.

cs.LG↗

arXiv2015

Probabilistic Clustering of Time-Evolving Distance Data

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the underlying cluster structure and obtain a smooth cluster evolution. This approach allows the number of objects and clusters to differ at every time point, and no identification on the identities of the objects is needed. Further, the model does not require the number of clusters being specified in advance -- they are instead determined automatically using a Dirichlet process prior. We validate our model on synthetic data showing that the proposed method is more accurate than state-of-the-art clustering methods. Finally, we use our dynamic clustering model to analyze and illustrate the evolution of brain cancer patients over time.

cs.LG↗

arXiv2014

Localized Complexities for Transductive Learning

We show two novel concentration inequalities for suprema of empirical processes when sampling without replacement, which both take the variance of the functions into account. While these inequalities may potentially have broad applications in learning theory in general, we exemplify their significance by studying the transductive setting of learning theory. For which we provide the first excess risk bounds based on the localized complexity of the hypothesis class, which can yield fast rates of convergence also in the transductive learning setting. We give a preliminary analysis of the localized complexities for the prominent case of kernel classes.

stat.ML↗

arXiv2011

Insights from Classifying Visual Concepts with Multiple Kernel Learning

Combining information from various image features has become a standard technique in concept recognition tasks. However, the optimal way of fusing the resulting kernel functions is usually unknown in practical applications. Multiple kernel learning (MKL) techniques allow to determine an optimal linear combination of such similarity matrices. Classical approaches to MKL promote sparse mixtures. Unfortunately, so-called 1-norm MKL variants are often observed to be outperformed by an unweighted sum kernel. The contribution of this paper is twofold: We apply a recently developed non-sparse MKL variant to state-of-the-art concept recognition tasks within computer vision. We provide insights on benefits and limits of non-sparse MKL and compare it against its direct competitors, the sum kernel SVM and the sparse MKL. We report empirical results for the PASCAL VOC 2009 Classification and ImageCLEF2010 Photo Annotation challenge data sets. About to be submitted to PLoS ONE.

cs.CV↗

arXiv2011

The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning

We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while our analysis covers all cases $1\leq p\leq\infty$, assuming the different feature mappings corresponding to the different kernels to be uncorrelated. We also show a lower bound that shows that the bound is tight, and derive consequences regarding excess loss, namely fast convergence rates of the order $O(n^{-\fracα{1+α}})$, where $α$ is the minimum eigenvalue decay rate of the individual kernels.

stat.ML↗