The non-stationary nature of electroencephalography (EEG) introduces distribution shifts across domains (e.g., days and subjects), posing a significant challenge to EEG-based neurotechnology generalization. Without labeled calibration data for target domains, the problem is a source-free unsupervised domain adaptation (SFUDA) problem. For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks on the symmetric positive definite (SPD) manifold are considered state-of-the-art. However, many practical scenarios, including EEG-based sleep staging, exhibit label shifts. Here, we propose a geometric deep learning framework for SFUDA problems under specific distribution shifts, including label shifts. We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts. As a remedy, we propose a parameter-efficient manifold optimization strategy termed SPDIM. SPDIM uses the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain. In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model. Moreover, using public EEG-based brain-computer interface and sleep staging datasets, we show that SPDIM outperforms prior approaches.

We present a novel task for cross-dataset visual grounding in 3D scenes (Cross3DVG), which overcomes limitations of existing 3D visual grounding models, specifically their restricted 3D resources and consequent tendencies of overfitting a specific 3D dataset. We created RIORefer, a large-scale 3D visual grounding dataset, to facilitate Cross3DVG. It includes more than 63 k diverse descriptions of 3D objects within 1,380 indoor RGB-D scans from 3RScan [48], with human annotations. After training the Cross3DVG model using the source 3D visual grounding dataset, we evaluate it without target labels using the target dataset with, e.g., different sensors, 3D reconstruction methods, and language annotators. Comprehensive experiments are conducted using established visual grounding models and with CLIP-based multi-view 2D and 3D integration designed to bridge gaps among 3D datasets. For Cross3DVG tasks, (i) cross-dataset 3D visual grounding exhibits significantly worse performance than learning and evaluation with a single dataset because of the 3D data and language variants across datasets. Moreover, (ii) better object detector and localization modules and fusing 3D data and multi-view CLIP-based image features can alleviate this lower performance. Our Cross3DVG task can provide a benchmark for developing robust 3D visual grounding models to handle diverse 3D scenes while leveraging deep language understanding.11Project page: https://github.com/ATR-DBI/Cross3DVG

Electroencephalography (EEG) based brain-computer interfaces (BCIs) face great challenges in generalizing across different domains (i.e., sessions and subjects) without costly supervised calibration.To avoid supervised calibration, transfer learning, particularly unsupervised domain adaptation, has been a popular approach.In this work, we focus on a geometric deep learning framework previously proposed for EEG-based mental imagery BCIs.The framework aligns marginal feature distributions in latent space, assuming identical label distributions across domains.Here, we propose a novel approach integrating data augmentation and clustering techniques to align the latent distributions under label shifts.

In human neuroimaging, multi-modal imaging techniques are frequently combined to enhance our comprehension of whole-brain dynamics and improve diagnosis in clinical practice. Modalities like electroencephalography and functional magnetic resonance imaging provide distinct views to the brain dynamics due to diametral spatiotemporal sensitivities and underlying neurophysiological coupling mechanisms. These distinct views pose a considerable challenge to learning a shared representation space, especially when dealing with covariance-based data characterized by their geometric structure. To capitalize on the geometric structure, we introduce a measure called geodesic correlation which expands traditional correlation consistency to covariance-based data on the symmetric positive definite (SPD) manifold. This measure is derived from classical canonical correlation analysis and serves to evaluate the consistency of latent representations obtained from paired views. For multi-view, self-supervised learning where one or both latent views are SPD we propose an innovative geometric deep learning framework termed DeepGeoCCA. Its primary objective is to enhance the geodesic correlation of unlabeled, paired data, thereby generating novel representations while retaining the geometric structures. In simulations and experiments with multi-view and multi-modal human neuroimaging data, we find that DeepGeoCCA learns latent representations with high geodesic correlation for unseen data while retaining relevant information for downstream tasks.

We propose Answerability Fields (AnsFields), a novel approach for predicting the answerability of questions at different locations within indoor environments. AnsFields is represented as a map, where each grid’s score reflects how well a question can be answered using the panoramic image at that location. Using a 3D question-answering dataset, we construct comprehensive AnsFields covering diverse scenes from ScanNet. Additionally, we employ a diffusion model to infer AnsFields from a scene’s top-down view image and the question. We then conduct 3D question-answering using these predicted AnsFields and achieve a 24% improvement in accuracy over the standard 3D-QA method. Our results demonstrate the importance of object locations for answering questions in the environment, highlighting the potential of AnsFields for applications in robotics, augmented reality, and human-robot interaction.

Embodied Question Answering (EQA) serves as a benchmark task to evaluate the capability of robots to navigate within novel environments and identify objects in response to human queries. However, existing EQA methods often rely on simulated environments and operate with limited vocabularies. This paper presents a map-based modular approach to EQA, enabling real-world robots to explore and map unknown environments. By leveraging foundation models, our method facilitates answering a diverse range of questions using natural language. We conducted extensive experiments in both virtual and real-world settings, demonstrating the robustness of our approach in navigating and comprehending queries within unknown environments.

City-scale 3D point cloud is a promising way to express detailed and complicated outdoor structures. It encompasses both the appearance and geometry features of segmented city components, including cars, streets, and buildings that can be utilized for attractive applications such as user-interactive navigation of autonomous vehicles and drones. However, compared to the extensive text annotations available for images and indoor scenes, the scarcity of text annotations for outdoor scenes poses a significant challenge for achieving these applications. To tackle this problem, we introduce the CityRefer dataset for city-level visual grounding. The dataset consists of 35k natural language descriptions of 3D objects appearing in SensatUrban city scenes and 5k landmarks labels synchronizing with OpenStreetMap. To ensure the quality and accuracy of the dataset, all descriptions and labels in the CityRefer dataset are manually verified. We also have developed a baseline system that can learn encoded language descriptions, 3D object instances, and geographical information about the city's landmarks to perform visual grounding on the CityRefer dataset. To the best of our knowledge, the CityRefer dataset is the largest city-level visual grounding dataset for localizing specific 3D objects.

We propose a new 3D spatial understanding task for 3D question answering (3D-QA). In the 3D-QA task, models receive visual information from the entire 3D scene of a rich RGB-D indoor scan and answer given textual questions about the 3D scene. Unlike the 2D-question answering of visual question answering, the conventional 2D-QA models suffer from problems with spatial understanding of object alignment and directions and fail in object localization from the textual questions in 3D-QA. We propose a baseline model for 3D-QA, called the ScanQA11https://github.com/ATR-DBI/ScanQA, which learns a fused descriptor from 3D object proposals and encoded sentence embeddings. This learned descriptor correlates language expressions with the underlying geometric features of the 3D scan and facilitates the regression of 3D bounding boxes to determine the described objects in textual questions. We collected human-edited question-answer pairs with free-form answers grounded in 3D objects in each 3D scene. Our new ScanQA dataset contains over 41k question-answer pairs from 800 indoor scenes obtained from the ScanNet dataset. To the best of our knowledge, ScanQA is the first large-scale effort to perform object-grounded question answering in 3D environments.

Symmetric positive definite (SPD) matrices, and in particular co-variance matrices as data descriptors find widespread application in various fields but also pure machine learning. SPD matrices form a Riemannian manifold, demanding machine learning methods that take this structure into account. In this work, we extend upon previous works and propose a batch normalization algorithm for the SPD manifold that can be readily combined with SPD neural networks and unlike previous works controls both the Fréchet mean and variance on the SPD manifold. The proposed method is validated in simulations and datasets with small sample sizes from three application domains: action recognition from human motion trajectories, image classification and mental imagery detection of electroencephalographic (EEG) signals. The combined results show a systematic performance increase upon previous works and tangent space approximations, as well as improved robustness to low signal-to-noise ratios and lack of data as often encountered in neuroimaging and brain-computer interfacing (BCI).

Electroencephalography (EEG) provides access to neuronal dynamics non-invasively with millisecond resolution, rendering it a viable method in neuroscience and healthcare. However, its utility is limited as current EEG technology does not generalize well across domains (i.e., sessions and subjects) without expensive supervised re-calibration. Contemporary methods cast this transfer learning (TL) problem as a multi-source/-target unsupervised domain adaptation (UDA) problem and address it with deep learning or shallow, Riemannian geometry aware alignment methods. Both directions have, so far, failed to consistently close the performance gap to state-of-the-art domain-specific methods based on tangent space mapping (TSM) on the symmetric, positive definite (SPD) manifold.Here, we propose a machine learning framework that enables, for the first time, learning domain-invariant TSM models in an end-to-end fashion. To achieve this, we propose a new building block for geometric deep learning, which we denote SPD domain-specific momentum batch normalization (SPDDSMBN). A SPDDSMBN layer can transform domain-specific SPD inputs into domain-invariant SPD outputs, and can be readily applied to multi-source/-target and online UDA scenarios. In extensive experiments with 6 diverse EEG brain-computer interface (BCI) datasets, we obtain state-of-the-art performance in inter-session and -subject TL with a simple, intrinsically interpretable network architecture, which we denote TSMNet. Code: https://github.com/rkobler/TSMNet

We present a method to predict humans in unexplored map areas given limited observations of the environment. We used a geometric representation of the environment based on cost maps and semantic room categorization. Human density distributions were generated using a human tracker based on LiDAR data recorded by a mobile robot. A Gaussian Process (GP) regression model was created to predict human density in surrounding unobserved map locations. GP prediction performance was evaluated on density data recorded in a series of ten simulations of 25 persons in an office setting, and in real-world robot deployments in an office-like environment. Experimental results demonstrate that the current method can predict human locations with an accuracy average of 70%.

Recognizing activities of daily living (ADLs) in the real world is an important task for understanding everyday human life. However, even though our life events consist of chronological ADLs with the corresponding places and objects (e.g., drinking coffee in the living room after making coffee in the kitchen and walking to the living room), most existing works focus on predicting individual activity labels from sensor data. In this paper, we introduce a novel framework that produces an event timeline of ADLs in a home environment. The proposed method combines semantic concepts such as action, object, and place detected by sensors for generating stereotypical event sequences with the following three real-world properties. First, we use temporal interactions among concepts to remove objects and places unrelated to each action. Second, we use commonsense knowledge mined from a language resource to find a possible combination of concepts in the real world. Third, we use temporal variations of events to filter repetitive events, since our daily life changes over time. We use cross-place validation to evaluate our proposed method on a daily-activities dataset with manually labeled event descriptions. The empirical evaluation demonstrates that our method using real-world properties improves the performance of generating an event timeline over diverse environments.

To efficiently process and understand a large amount of incoming visual information from first-person perspective (i.e. egocentric vision), predicting human gaze is important. However, even though people continuously gaze in noisy environments, most existing gaze prediction methods mainly use image saliency, which is sensitive to noise in the real-world. To address this issue, we propose a sparse coding-based saliency detection method for gaze prediction. Our model uses a cost function with the 10 norm as a sparse constraint that can control the area of visual saliency in response to the contents of egocentric vision in intuitive and consistent ways. Moreover, we use canonical correlation analysis (CCA) to combine different types of features for reducing noise and the computational complexity. We also utilize the temporal continuity of image frames when defining our saliency. Experiments using a real-world gaze dataset show that our proposed approach outperforms the state-of-the-art algorithms on gaze prediction in egocentric videos.

We propose a physical-world question-answering (QA) method, where the system answers a text question about the physical world by searching a given sequence of sentences about daily-life episodes. To address various information needs in a physical world situation, the physical-world QA methods have to generate mixed-type responses (e.g. word sequence, word set, number, and time as well as a single word) according to the content of questions, after reading physical-world event stories. Most existing methods only provide words or choose answers from multiple candidates. In this paper, we use multiple decoders to generate a mixed-type answer encoding daily episodes with a memory architecture that can capture short- and long-term event dependencies. Results using house-activity stories show that the use of multiple decoders with memory components is effective for answering various physical-world QA questions.

We introduce a framework for detection and classification of spatio-temporal person-object interactions. Our method clusters similar semantic contexts from interactions detected from RGB-D data. 2-D object detection (YOLO) is run on RGB data from a Kinect v2 sensor on a mobile robot navigating an office and observing persons and desk spaces. Person and object detections are converted into 3-D point cloud time series via RGB-Depth co-registration and successive Euclidean and k-means spatial clustering. 3-D person and object point cloud streams are used to create time-series occupancy maps and person-object co-localization maps. From these maps, spatiotemporal correlations between persons and distinct objects are computed. Correlation patterns are clustered using k-means to obtain distinct human-object interactions, i.e. segment semantic context over time. We evaluated the performance of our approach to detect person-object correlations and cluster semantic context by recording 90 30-second RGB-D data episodes, with three persons handling representative objects (books, cups, bottles). Experimental results show that our framework is able to consistently assign semantic context to the same cluster in > 79% of cases (scene frames). Semantic contexts in visual scenes can be distinguished without the need to provide prior information, allowing mobile agents to learn and explore in new environments.

Selecting authentic scenes about activities of daily living (ADL) is useful to support our memory of everyday life. Key-frame extraction for first-person vision (FPV) videos is a core technology to realize such memory assistant. However, most existing key-frame extraction methods have mainly focused on stable scenes not related to ADL and only used visual signals of the image sequence even though the activities usually associate with our visual experience. To deal with dynamically changing scenes of FPV about daily activities, integrating motion and visual signals are essential. In this paper, we present a novel key-frame extraction method for ADL, which integrates multi-modal sensor signals to temper noise and detect salient activities. Our proposed method projects motion and visual features to a shared space by a probabilistic canonical correlation analysis and selects key frames there. The experimental results using ADL datasets collected in a house suggest that our key-frame extraction technique running in the shared space improves the precision of extracted key frames and the coverage of the entire video.

First-person videos (FPVs) in daily living help us to memorize our life experience and information systems to process daily activities. Summarizing FPVs into key frames that represent the entire data would allow us to remember our memory in the past and computers to efficiently process the data. However, most video summarization approaches only use visual information, even though our daily activities consist of multiple modalities such as movements and sounds. FPVs are not as stable as movies or sport scenes since the camera attached to the head shakes frequently, and key frame extraction methods rely only on video frames do not always produce satisfactory results. In this paper, we introduce a novel key frame extraction method for FPVs using multiple wearable sensors. To efficiently integrate multimodal sensor signals, our formulation uses sparse dictionary selection, which minimizes a reconstruction error with a subset (key frames) of the original data. We present experimental results with multimodal datasets captured by wearable sensors in a natural environment. The results suggest multi-sensor information improves the precision of extracted key frames as well as the coverage of an entire video sequence.

We present a novel probabilistic framework for a hierarchical extension of independent component analysis (ICA), with a particular motivation in neuroscientific data analysis and modeling. The framework incorporates a general subspace pooling with linear ICA-like layers stacked recursively. Unlike related previous models, our generative model is fully tractable: both the likelihood and the posterior estimates of latent variables can readily be computed with analytically simple formulae. The model is particularly simple in the case of complex-valued data since the pooling can be reduced to taking the modulus of complex numbers. Experiments on electroencephalography (EEG) and natural images demonstrate the validity of the method.

In many multivariate time series, the correlation structure is nonstationary, that is, it changes over time. The correlation structure may also change as a function of other cofactors, for example, the identity of the subject in biomedical data. A fundamental approach for the analysis of such data is to estimate the correlation structure (connectivities) separately in short time windows or for different subjects and use existing machine learning methods, such as principal component analysis (PCA), to summarize or visualize the changes in connectivity. However, the visualization of such a straightforward PCA is problematic because the ensuing connectivity patterns are much more complex objects than, say, spatial patterns. Here, we develop a new framework for analyzing variability in connectivities using the PCA approach as the starting point. First, we show how to analyze and visualize the principal components of connectivity matrices by a tailor-made rank-two matrix approximation in which we use the outer product of two orthogonal vectors. This leads to a new kind of transformation of eigenvectors that is particularly suited for this purpose and often enables interpretation of the principal component as connectivity between two groups of variables. Second, we show how to incorporate the orthogonality and the rank-two constraint in the estimation of PCA itself to improve the results. We further provide an interpretation of these methods in terms of estimation of a probabilistic generative model related to blind separation of dependent sources. Experiments on brain imaging data give very promising results.

Reliable estimation of covariance matrices from high-dimensional electroencephalographic recordings is crucial for a successful application of Brain-Computer Interface (BCI) systems. Artifactual trials and non-stationarity effects may have a large impact on the estimation quality and adversely affect the spatial filter computation and consequently the classification accuracy of the system. In this work we propose a novel robust estimator for covariance matrices that takes into account the trial structure of BCI experiments. Our estimator minimizes beta divergence between the empirical and a model Wishart distribution, thus allows to robustly average the estimated covariance matrices of different trials and downweight the influence of outlier trials. We evaluate this novel estimator on a data set with recordings from 80 subjects.

Electroencephalographic signals are known to be nonstationary and easily affected by artifacts; therefore, their analysis requires methods that can deal with noise. In this work, we present a way to robustify the popular common spatial patterns (CSP) algorithm under a maxmin approach. In contrast to standard CSP that maximizes the variance ratio between two conditions based on a single estimate of the class covariance matrices, we propose to robustly compute spatial filters by maximizing the minimum variance ratio within a prefixed set of covariance matrices called the tolerance set. We show that this kind of maxmin optimization makes CSP robust to outliers and reduces its tendency to overfit. We also present a data-driven approach to construct a tolerance set that captures the variability of the covariance matrices over time and shows its ability to reduce the nonstationarity of the extracted features and significantly improve classification accuracy. We test the spatial filters derived with this approach and compare them to standard CSP and a state-of-the-art method on a real-world brain-computer interface (BCI) data set in which we expect substantial fluctuations caused by environmental differences. Finally we investigate the advantages and limitations of the maxmin approach with simulations.

The noninvasive brain-machine interface (BMI) is anticipated to be an effective tool of communication not only in laboratory settings but also in our daily livings. The direct communication channel created by BMI can assist aging societies and the handicapped and improve human welfare. In this paper we propose and experiment a BMI framework that combines BMI with a robotic house and autonomous robotic wheelchair. Autonomous navigation is achieved by placing waypoints within the house and, from the user side, the user performs BMI to give commands to the house and wheelchair. The waypoint framework can offer essential services to the user with an effectively improved information-transfer rate and is an excellent examples of the fusion of data measured by sensors in the house, which can offer insight into further studies.

The efficiency of Brain-Computer Interfaces (BCI) largely depends upon a reliable extraction of informative features from the high-dimensional EEG signal. A crucial step in this protocol is the computation of spatial filters. The Common Spatial Patterns (CSP) algorithm computes filters that maximize the difference in band power between two conditions, thus it is tailored to extract the relevant information in motor imagery experiments. However, CSP is highly sensitive to artifacts in the EEG data, i.e. few outliers may alter the estimate drastically and decrease classification performance. Inspired by concepts from the field of information geometry we propose a novel approach for robustifying CSP. More precisely, we formulate CSP as a divergence maximization problem and utilize the property of a particular type of divergence, namely beta divergence, for robustifying the estimation of spatial filters in the presence of artifacts in the data. We demonstrate the usefulness of our method on toy data and on EEG recordings from 80 subjects.

We study the problem of classifying images into a given, pre-determined taxonomy. This task can be elegantly translated into the structured learning framework. However, despite its power, structured learning has known limits in scalability due to its high memory requirements and slow training process. We propose an efficient approximation of the structured learning approach by an ensemble of local support vector machines (SVMs) that can be trained efficiently with standard techniques. A first theoretical discussion and experiments on toy-data allow to shed light onto why taxonomy-based classification can outperform taxonomy-free approaches and why an appropriately combined ensemble of local SVMs might be of high practical use. Further empirical results on subsets of Caltech256 and VOC2006 data indeed show that our local SVM formulation can effectively exploit the taxonomy structure and thus outperforms standard multi-class classification algorithms while it achieves on par results with taxonomy-based structured algorithms at a significantly decreased computing time.

Brain-Computer Interfaces (BCIs) allow a user to control a computer application by brain activity as acquired, e.g., by EEG. A standard step in a BCI system is to project the EEG signals to a low-dimensional subspace using Common Spatial Patterns (CSP). However, non-stationarities in the data can negatively affect the performance of CSP, i.e. variation of the signal properties within and across experimental sessions coming from electrode artefacts, alpha or muscular activity, or fatigue may result in suboptimal projection directions. We alleviate this problem by regularizing CSP towards stationary subspaces and show that this especially increases classification accuracy of people who are not able to control a BCI i.e. have more than 30% of error. These users very often show non-stationarities in their EEG signals.

Automatic annotation of images is a challenging task in computer vision because of “semantic gap” between highlevel visual concepts and image appearances. Therefore, user tags attached to images can provide further information to bridge the gap, even though they are partially uninformative and misleading. In this work, we investigate multi-modal visual concept classification based on visual features and user tags via kernel-based classifiers. An issue here is how to construct kernels between sets of tags. We deploy Markov random walks on graphs of key tags to incorporate co-occurrence between them. This procedure acts as a smoothing of tag based features. Our experimental result on the ImageCLEF2010 PhotoAnnotation benchmark shows that our proposed method outperforms the baseline relying solely on visual information and a recently published state-of-the-art approach.

The quality of visual vocabularies is crucial for the performance of bag-of-words image classification methods. Several approaches have been developed for codebook construction, the most popular method is to cluster a set of image features (e.g. SIFT) by k-means. In this paper, we propose a two-step procedure which incorporates label information into the clustering process by efficiently generating a large and informative vocabulary using class-wise k-means and reducing its size by agglomerative information bottleneck (AIB). We introduce an extension of the AIB procedure for multi-label problems and show that this two-step approach improves the classification results while reducing computation time compared to the vanilla k-means. We analyse the reasons for the performance gain on the PASCAL VOC 2007 data set.

In recent years bag-of-visual-words representations have gained increasing popularity in the field of image classification. Their performance highly relies on creating a good visual vocabulary from a set of image features (e.g. SIFT). For real-world photo archives such as Flicker, codebooks with larger than a few thousand words are desirable, which is infeasible by the standard k-means clustering. In this paper, we propose a two-step procedure which can generate more informative codebooks efficiently by class-wise k-means and a novel procedure for word selection. Our approach was compared favorably to the standard k-means procedure on the PASCAL VOC data sets.

Methods for directly estimating the ratio of two probability density functions without going through density estimation have been actively explored recently since they can be used for various data processing tasks such as non-stationarity adaptation, outlier detection, conditional density estimation, feature selection, and independent component analysis. However, even the state-of-the-art density ratio estimation methods still perform rather poorly in high-dimensional problems. In this paper, we propose a new density ratio estimation method which incorporates dimensionality reduction into a density ratio estimation procedure. Our key idea is to identify a low-dimensional subspace in which the two densities corresponding to the denominator and the numerator in the density ratio are significantly different. Then the density ratio is estimated only within this low-dimensional subspace. Through numerical examples, we illustrate the effectiveness of the proposed method.

Reinforcement learning (RL) methods based on least-squares temporal difference (LSTD) have been developed recently and have shown good practical performance. However, the quality of their estimation has not been well elucidated. In this article, we discuss LSTD-based policy evaluation from the new view-point of semiparametric statistical inference. In fact, the estimator can be obtained from a particular estimating function which guarantees its convergence to the true value asymptotically, without specifying a model of the environment. Based on these observations, we 1) analyze the asymptotic variance of an LSTD-based estimator, 2) derive the optimal estimating function with the minimum asymptotic estimation variance, and 3) derive a suboptimal estimator to reduce the computational burden in obtaining the optimal estimating function.

In supervised learning, we commonly assume that training and test data are sampled from the same distribution. However, this assumption can be violated in practice and then standard machine learning techniques perform poorly. This paper focuses on revealing and improving the performance of Bayesian estimation when the training and test distributions are different. We formally analyze the asymptotic Bayesian generalization error and establish its upper bound under a very general setting. Our important finding is that lower order terms---which can be ignored in the absence of the distribution change---play an important role under the distribution change. We also propose a novel variant of stochastic complexity which can be used for choosing an appropriate model and hyper-parameters under a particular distribution change.

Brain-Computer Interfaces can suffer from a large variance of the subject condi- tions within and across sessions. For example vigilance fluctuations in the indi- vidual, variable task involvement, workload etc. alter the characteristics of EEG signals and thus challenge a stable BCI operation. In the present work we aim to define features based on a variant of the common spatial patterns (CSP) algorithm that are constructed invariant with respect to such nonstationarities. We enforce invariance properties by adding terms to the denominator of a Rayleigh coefficient representation of CSP such as disturbance covariance matrices from fluctuations in visual processing. In this manner physiological prior knowledge can be used to shape the classification engine for BCI. As a proof of concept we present a BCI classifier that is robust to changes in the level of parietal a -activity. In other words, the EEG decoding still works when there are lapses in vigilance.

In bioinformatics it is often desirable to combine data from various measurement sources and thus structured feature vectors are to be analyzed that possess different intrinsic blocking characteristics (e.g., different patterns of missing values, obser- vation noise levels, effective intrinsic dimensionalities). We propose a new ma- chine learning tool, heterogeneous component analysis (HCA), for feature extrac- tion in order to better understand the factors that underlie such complex structured heterogeneous data. HCA is a linear block-wise sparse Bayesian PCA based not only on a probabilistic model with block-wise residual variance terms but also on a Bayesian treatment of a block-wise sparse factor-loading matrix. We study vari- ous algorithms that implement our HCA concept extracting sparse heterogeneous structure by obtaining common components for the blocks and specific compo- nents within each block. Simulations on toy and bioinformatics data underline the usefulness of the proposed structured matrix factorization concept.

When training and test samples follow different input distributions (i.e., the situation called \emph{covariate shift}), the maximum likelihood estimator is known to lose its consistency. For regaining consistency, the log-likelihood terms need to be weighted according to the \emph{importance} (i.e., the ratio of test and training input densities). Thus, accurately estimating the importance is one of the key tasks in covariate shift adaptation. A naive approach is to first estimate training and test input densities and then estimate the importance by the ratio of the density estimates. However, since density estimation is a hard problem, this approach tends to perform poorly especially in high dimensional cases. In this paper, we propose a direct importance estimation method that does not require the input density estimates. Our method is equipped with a natural model selection procedure so tuning parameters such as the kernel width can be objectively optimized. This is an advantage over a recently developed method of direct importance estimation. Simulations illustrate the usefulness of our approach.

Obtaining the best linear unbiased estimator (BLUE) of noisy signals is a traditional but powerful approach to noise reduction. Explicitly computing BLUE usually requires the prior knowledge of the subspace to which the true signal belongs and the noise covariance matrix. However, such prior knowledge is often unavailable in reality, which prevents us from applying BLUE to real-world problems. In this paper, we therefore give a method for obtaining BLUE without such prior knowledge. Our additional assumption is that the true signal follows a non-Gaussian distribution while the noise is Gaussian

Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the "non-Gaussian subspace" within a very general semi-parametric framework. Our proposed method, called NGCA (non-Gaussian component analysis), is based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector belonging to the low dimensional non-Gaussian target subspace, up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.

We propose a new linear method for dimension reduction to identify nonGaussian components in high dimensional data. Our method, NGCA (non-Gaussian component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (Gaussian): by projecting out uninterestingness, we can estimate the relevant non-Gaussian subspace. We show that the estimation error of finding the non-Gaussian components tends to zero at a parametric rate. Once NGCA components are identified and extracted, various tasks can be applied in the data analysis process, like data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.

A blind separation problem where the sources are not independent, but have variance dependencies is discussed. For this scenario Hyvärinen and Hurri (2004) proposed an algorithm which requires no assumption on distributions of sources and no parametric model of dependencies between components. In this paper, we extend the semiparametric approach of Amari and Cardoso (1997) to variance dependencies and study estimating functions for blind separation of such dependent sources. In particular, we show that many ICA algorithms are applicable to the variance-dependent model as well under mild conditions, although they should in principle not. Our results indicate that separation can be done based only on normalized sources which are adjusted to have stationary variances and is not affected by the dependent activity levels. We also study the asymptotic distribution of the quasi maximum likelihood method and the stability of the natural gradient learning in detail. Simulation results of artificial and realistic examples match well with our theoretical findings.

A well-known result by Stein (1956) shows that in particular situations, biased estimators can yield better parameter estimates than their generally preferred unbiased counterparts. This letter follows the same spirit, as we will stabilize the unbiased generalization error estimates by regularization and finally obtain more robust model selection criteria for learning. We trade a small bias against a larger variance reduction, which has the beneficial effect of being more precise on a single training set. We focus on the subspace information criterion (SIC), which is an unbiased estimator of the expected generalization error measured by the reproducing kernel Hilbert space norm. SIC can be applied to the kernel regression, and it was shown in earlier experiments that a small regularization of SIC has a stabilization effect. However, it remained open how to appropriately determine the degree of regularization in SIC. In this article, we derive an unbiased estimator of the expected squared error, between SIC and the expected generalization error and propose determining the degree of regularization of SIC such that the estimator of the expected squared error is minimized. Computer simulations with artificial and real data sets illustrate that the proposed method works effectively for improving the precision of SIC, especially in the high-noise-level cases. We furthermore compare the proposed method to the original SIC, the cross-validation, and an empirical Bayesian method in ridge parameter selection, with good results.

This letter analyzes the Fisher kernel from a statistical point of view. The Fisher kernel is a particularly interesting method for constructing a model of the posterior probability that makes intelligent use of unlabeled data (i.e., of the underlying data density). It is important to analyze and ultimately understand the statistical properties of the Fisher kernel. To this end, we first establish sufficient conditions that the constructed posterior model is realizable (i.e., it contains the true distribution). Realizability immediately leads to consistency results. Subsequently, we focus on an asymptotic analysis of the generalization error, which elucidates the learning curves of the Fisher kernel and how unlabeled data contribute to learning. We also point out that the squared or log loss is theoretically preferable-because both yield consistent estimators-to other losses such as the exponential loss, when a linear classifier is used together with the Fisher kernel. Therefore, this letter underlines that the Fisher kernel should be viewed not as a heuristics but as a powerful statistical tool with well-controlled statistical properties.

We propose kTDSEP, a kernel-based algorithm for nonlinear blind source separation (BSS). It combines complementary research fields: kernel feature spaces and BSS using temporal information. This yields an efficient algorithm for nonlinear BSS with invertible nonlinearity. Key assumptions are that the kernel feature space is chosen rich enough to approximate the nonlinearity and that signals of interest contain temporal information. Both assumptions are fulfilled for a wide set of real-world applications. The algorithm works as follows: First, the data are (implicitly) mapped to a high (possibly infinite)—dimensional kernel feature space. In practice, however, the data form a smaller submanifold in feature space—even smaller than the number of training data points—a fact that has already been used by, for example, reduced set techniques for support vector machines. We propose to adapt to this effective dimension as a preprocessing step and to construct an orthonormal basis of this submanifold. The latter dimension-reduction step is essential for making the subsequent application of BSS methods computationally and numerically tractable. In the reduced space, we use a BSS algorithm that is based on second-order temporal decorrelation. Finally, we propose a selection procedure to obtain the original sources from the extracted nonlinear components automatically. Experiments demonstrate the excellent performance and efficiency of our kTDSEP algorithm for several problems of nonlinear BSS and for more than two sources.

For several major applications of data analysis, objects are often not represented as feature vectors in a vector space, but rather by a matrix gathering pairwise proximities. Such pairwise data often violates metricity and, therefore, cannot be naturally embedded in a vector space. Concerning the problem of unsupervised structure detection or clustering, in this paper, a new embedding method for pairwise data into Euclidean vector spaces is introduced. We show that all clustering methods, which are invariant under additive shifts of the pairwise proximities, can be reformulated as grouping problems in Euclidian spaces. The most prominent property of this constant shift embedding framework is the complete preservation of the cluster structure in the embedding space. Restating pairwise clustering problems in vector spaces has several important consequences, such as the statistical description of the clusters by way of cluster prototypes, the generic extension of the grouping procedure to a discriminative prediction rule, and the applicability of standard preprocessing methods like denoising or dimensionality reduction.

Recently the Fisher score (or the Fisher kernel) is increasingly used as a feature extractor for classification problems. The Fisher score is a vector of parameter derivatives of loglikelihood of a probabilistic model. This paper gives a theoretical analysis about how class information is pre- served in the space of the Fisher score, which turns out that the Fisher score consists of a few important dimensions with class information and many nuisance dimensions. When we perform clustering with the Fisher score, K-Means type methods are obviously inappropriate because they make use of all dimensions. So we will develop a novel but simple clus- tering algorithm specialized for the Fisher score, which can exploit im- portant dimensions. This algorithm is successfully tested in experiments with artificial data and real data (amino acid sequences). as follows: Let us assume that a probabilistic model   parameter estimate 

Recently, Jaakkola and Haussler (1999) proposed a method for constructing kernel functions from probabilistic models. Their so-called Fisher kernel has been combined with discriminative classifiers such as support vector machines and applied successfully in, for example, DNA and protein analysis. Whereas the Fisher kernel is calculated from the marginal log-likelihood, we propose the TOP kernel derived; from tangent vectors of posterior log-odds. Furthermore, we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing the TOP kernel. In experiments, our new discriminative TOP kernel compares favorably to the Fisher kernel.

In kernel based learning the data is mapped to a kernel feature space of a dimension that corresponds to the number of training data points. In practice, however, the data forms a smaller submanifold in feature space, a fact that has been used e.g. by reduced set techniques for SVMs. We propose a new mathematical construction that permits to adapt to the in- trinsic dimension and to find an orthonormal basis of this submanifold. In doing so, computations get much simpler and more important our theoretical framework allows to derive elegant kernelized blind source separation (BSS) algorithms for arbitrary invertible nonlinear mixings. Experiments demonstrate the good performance and high computational efficiency of our kTDSEP algorithm for the problem of nonlinear BSS.

When applying unsupervised learning techniques like ICA or tem(cid:173) poral decorrelation, a key question is whether the discovered pro(cid:173) jections are reliable. In other words: can we give error bars or can we assess the quality of our separation? We use resampling meth(cid:173) ods to tackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the sepa(cid:173) ration error. We demonstrate that this reliability estimation can be used to choose the appropriate ICA-model, to enhance signifi(cid:173) cantly the separation performance, and, most important, to mark the components that have a actual physical meaning. Application to 49-channel-data from an magneto encephalography (MEG) ex(cid:173) periment underlines the usefulness of our approach.

Recently, Jaakkola and Haussler proposed a method for construct(cid:173) ing kernel functions from probabilistic models. Their so called "Fisher kernel" has been combined with discriminative classifiers such as SVM and applied successfully in e.g. DNA and protein analysis. Whereas the Fisher kernel (FK) is calculated from the marginal log-likelihood, we propose the TOP kernel derived from Tangent vectors Of Posterior log-odds. Furthermore we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing FK and TOP. In experiments our new discriminative TOP kernel compares favorably to the Fisher kernel.

It was reported (Kabashima and Shinomoto 1992) that estimators of a binary decision boundary show asymptotically strange behaviors when the probability model is ill-posed or semiparametric. We give a rigorous analysis of this phenomenon in a stochastic perceptron by using the estimating function method. A stochastic perceptron consists of a neuron that is excited depending on the weighted sum of inputs but its probability distribution form is unknown here. It is shown that there exists no √n-consistent estimator of the threshold value h, that is, no estimator h that converges to h in the order of 1/ √n as the number n of observations increases. Therefore, the accuracy of estimation is much worse in this semiparametric case with an unspecified probability function than in the ordinary case. On the other hand, it is shown that there is a √n-consistent estimator ŵ of the synaptic weight vector. These results elucidate strange behaviors of learning curves in a semiparametric statistical model.