Freddie Kalaitzis

Vanessa Boehm, Wei Ji Leong, Ragini Bal Mahesh et al. · cmu, nvidia

With climate change predicted to increase the likelihood of landslide events, there is a growing need for rapid landslide detection technologies that help inform emergency responses. Synthetic Aperture Radar (SAR) is a remote sensing technique that can provide measurements of affected areas independent of weather or lighting conditions. Usage of SAR, however, is hindered by domain knowledge that is necessary for the pre-processing steps and its interpretation requires expert knowledge. We provide simplified, pre-processed, machine-learning ready SAR datacubes for four globally located landslide events obtained from several Sentinel-1 satellite passes before and after a landslide triggering event together with segmentation maps of the landslides. From this dataset, using the Hokkaido, Japan datacube, we study the feasibility of SAR-based landslide detection with supervised deep learning (DL). Our results demonstrate that DL models can be used to detect landslides from SAR data, achieving an Area under the Precision-Recall curve exceeding 0.7. We find that additional satellite visits enhance detection performance, but that early detection is possible when SAR data is combined with terrain information from a digital elevation model. This can be especially useful for time-critical emergency interventions. Code is made publicly available at https://github.com/iprapas/landslide-sar-unet.

Vanessa Böhm, Wei Ji Leong, Ragini Bal Mahesh et al. · cmu, nvidia

Rapid assessment after a natural disaster is key for prioritizing emergency resources. In the case of landslides, rapid assessment involves determining the extent of the area affected and measuring the size and location of individual landslides. Synthetic Aperture Radar (SAR) is an active remote sensing technique that is unaffected by weather conditions. Deep Learning algorithms can be applied to SAR data, but training them requires large labeled datasets. In the case of landslides, these datasets are laborious to produce for segmentation, and often they are not available for the specific region in which the event occurred. Here, we study how deep learning algorithms for landslide segmentation on SAR products can benefit from pretraining on a simpler task and from data from different regions. The method we explore consists of two training stages. First, we learn the task of identifying whether a SAR image contains any landslides or not. Then, we learn to segment in a sparsely labeled scenario where half of the data do not contain landslides. We test whether the inclusion of feature embeddings derived from stage-1 helps with landslide detection in stage-2. We find that it leads to minor improvements in the Area Under the Precision-Recall Curve, but also to a significantly lower false positive rate in areas without landslides and an improved estimate of the average number of landslide pixels in a chip. A more accurate pixel count allows to identify the most affected areas with higher confidence. This could be valuable in rapid response scenarios where prioritization of resources at a global scale is important. We make our code publicly available at https://github.com/VMBoehm/SAR-landslide-detection-pretraining.

Julien Cornebise, Ivan Oršolić, Freddie Kalaitzis

Analyzing the planet at scale with satellite imagery and machine learning is a dream that has been constantly hindered by the cost of difficult-to-access highly-representative high-resolution imagery. To remediate this, we introduce here the WorldStrat dataset. The largest and most varied such publicly available dataset, at Airbus SPOT 6/7 satellites' high resolution of up to 1.5 m/pixel, empowered by European Space Agency's Phi-Lab as part of the ESA-funded QueryPlanet project, we curate nearly 10,000 sqkm of unique locations to ensure stratified representation of all types of land-use across the world: from agriculture to ice caps, from forests to multiple urbanization densities. We also enrich those with locations typically under-represented in ML datasets: sites of humanitarian interest, illegal mining sites, and settlements of persons at risk. We temporally-match each high-resolution image with multiple low-resolution images from the freely accessible lower-resolution Sentinel-2 satellites at 10 m/pixel. We accompany this dataset with an open-source Python package to: rebuild or extend the WorldStrat dataset, train and infer baseline algorithms, and learn with abundant tutorials, all compatible with the popular EO-learn toolbox. We hereby hope to foster broad-spectrum applications of ML to satellite imagery, and possibly develop from free public low-resolution Sentinel2 imagery the same power of analysis allowed by costly private high-resolution imagery. We illustrate this specific point by training and releasing several highly compute-efficient baselines on the task of Multi-Frame Super-Resolution. High-resolution Airbus imagery is CC BY-NC, while the labels and Sentinel2 imagery are CC BY, and the source code and pre-trained models under BSD. The dataset is available at https://zenodo.org/record/6810791 and the software package at https://github.com/worldstrat/worldstrat .

Vanessa Boehm, Wei Ji Leong, Ragini Bal Mahesh et al. · cmu, nvidia

This work aims to produce landslide density estimates using Synthetic Aperture Radar (SAR) satellite imageries to prioritise emergency resources for rapid response. We use the United States Geological Survey (USGS) Landslide Inventory data annotated by experts after Hurricane María in Puerto Rico on Sept 20, 2017, and their subsequent susceptibility study which uses extensive additional information such as precipitation, soil moisture, geological terrain features, closeness to waterways and roads, etc. Since such data might not be available during other events or regions, we aimed to produce a landslide density map using only elevation and SAR data to be useful to decision-makers in rapid response scenarios. The USGS Landslide Inventory contains the coordinates of 71,431 landslide heads (not their full extent) and was obtained by manual inspection of aerial and satellite imagery. It is estimated that around 45\% of the landslides are smaller than a Sentinel-1 typical pixel which is 10m $\times$ 10m, although many are long and thin, probably leaving traces across several pixels. Our method obtains 0.814 AUC in predicting the correct density estimation class at the chip level (128$\times$128 pixels, at Sentinel-1 resolution) using only elevation data and up to three SAR acquisitions pre- and post-hurricane, thus enabling rapid assessment after a disaster. The USGS Susceptibility Study reports a 0.87 AUC, but it is measured at the landslide level and uses additional information sources (such as proximity to fluvial channels, roads, precipitation, etc.) which might not regularly be available in an rapid response emergency scenario.

Omar A. Castaño-Idarraga, Raul Ramos-Pollán, Freddie Kalaitzis

This work proposes a hybrid unsupervised and supervised learning method to pre-train models applied in Earth observation downstream tasks when only a handful of labels denoting very general semantic concepts are available. We combine a contrastive approach to pre-train models with a pixel-wise regression pre-text task to predict coarse elevation maps, which are commonly available worldwide. We hypothesize that this will allow the model to pre-learn useful representations, as there is generally some correlation between elevation maps and targets in many remote sensing tasks. We assess the performance of our approach on a binary semantic segmentation task and a binary image classification task, both derived from a dataset created for the northwest of Colombia. In both cases, we pre-train our models with 39k unlabeled images, fine-tune them on the downstream tasks with only 80 labeled images, and evaluate them with 2944 labeled images. Our experiments show that our methods, GLCNet+Elevation for segmentation, and SimCLR+Elevation for classification, outperform their counterparts without the pixel-wise regression pre-text task, namely SimCLR and GLCNet, in terms of macro-average F1 Score and Mean Intersection over Union (MIoU). Our study not only encourages the development of pre-training methods that leverage readily available geographical information, such as elevation data, to enhance the performance of self-supervised methods when applied to Earth observation tasks, but also promotes the use of datasets with high-level semantic labels, which are more likely to be updated frequently. Project code can be found in this link \href{https://github.com/omarcastano/Elevation-Aware-SSL}{https://github.com/omarcastano/Elevation-Aware-SSL}.

Karthick Panner Selvam, Raul Ramos-Pollan, Freddie Kalaitzis

This study investigates the efficacy of Low-Rank Adaptation (LoRA) in fine-tuning Earth Observation (EO) foundation models for flood segmentation. We hypothesize that LoRA, a parameter-efficient technique, can significantly accelerate the adaptation of large-scale EO models to this critical task while maintaining high performance. We apply LoRA to fine-tune a state-of-the-art EO foundation model pre-trained on diverse satellite imagery, using a curated dataset of flood events. Our results demonstrate that LoRA-based fine-tuning (r-256) improves F1 score by 6.66 points and IoU by 0.11 compared to a frozen encoder baseline, while significantly reducing computational costs. Notably, LoRA outperforms full fine-tuning, which proves computationally infeasible on our hardware. We further assess generalization through out-of-distribution (OOD) testing on a geographically distinct flood event. While LoRA configurations show improved OOD performance over the baseline. This work contributes to research on efficient adaptation of foundation models for specialized EO tasks, with implications for rapid response systems in disaster management. Our findings demonstrate LoRA's potential for enabling faster deployment of accurate flood segmentation models in resource-constrained, time-critical scenarios.

Raul Ramos-Pollan, Freddie Kalaitzis, Karthick Panner Selvam

We take the perspective in which we want to design a downstream task (such as estimating vegetation coverage) on a certain area of interest (AOI) with a limited labeling budget. By leveraging an existing Foundation Model (FM) we must decide whether we train a downstream model on a different but label-rich AOI hoping it generalizes to our AOI, or we split labels in our AOI for training and validating. In either case, we face choices concerning what FM to use, how to sample our AOI for labeling, etc. which affect both the performance and uncertainty of the results. In this work, we perform a large ablative study using eight existing FMs on either Sentinel 1 or Sentinel 2 as input data, and the classes from the ESA World Cover product as downstream tasks across eleven AOIs. We do repeated sampling and training, resulting in an ablation of some 500K simple linear regression models. Our results show both the limits of spatial generalizability across AOIs and the power of FMs where we are able to get over 0.9 correlation coefficient between predictions and targets on different chip level predictive tasks. And still, performance and uncertainty vary greatly across AOIs, tasks and FMs. We believe this is a key issue in practice, because there are many design decisions behind each FM and downstream task (input modalities, sampling, architectures, pretraining, etc.) and usually a downstream task designer is aware of and can decide upon a few of them. Through this work, we advocate for the usage of the methodology herein described (large ablations on reference global labels and simple probes), both when publishing new FMs, and to make informed decisions when designing downstream tasks to use them.

Matt Allen, Francisco Dorr, Joseph A. Gallego-Mejia et al.

Satellite-based remote sensing is instrumental in the monitoring and mitigation of the effects of anthropogenic climate change. Large scale, high resolution data derived from these sensors can be used to inform intervention and policy decision making, but the timeliness and accuracy of these interventions is limited by use of optical data, which cannot operate at night and is affected by adverse weather conditions. Synthetic Aperture Radar (SAR) offers a robust alternative to optical data, but its associated complexities limit the scope of labelled data generation for traditional deep learning. In this work, we apply a self-supervised pretraining scheme, masked autoencoding, to SAR amplitude data covering 8.7\% of the Earth's land surface area, and tune the pretrained weights on two downstream tasks crucial to monitoring climate change - vegetation cover prediction and land cover classification. We show that the use of this pretraining scheme reduces labelling requirements for the downstream tasks by more than an order of magnitude, and that this pretraining generalises geographically, with the performance gain increasing when tuned downstream on regions outside the pretraining set. Our findings significantly advance climate change mitigation by facilitating the development of task and region-specific SAR models, allowing local communities and organizations to deploy tailored solutions for rapid, accurate monitoring of climate change effects.

Matt Allen, Francisco Dorr, Joseph A. Gallego-Mejia et al.

In this work we pretrain a CLIP/ViT based model using three different modalities of satellite imagery across five AOIs covering over ~10\% of Earth's total landmass, namely Sentinel 2 RGB optical imagery, Sentinel 1 SAR radar amplitude and interferometric coherence. This model uses $\sim 250$ M parameters. Then, we use the embeddings produced for each modality with a classical machine learning method to attempt different downstream tasks for earth observation related to vegetation, built up surface, croplands and permanent water. We consistently show how we reduce the need for labeled data by 99\%, so that with ~200-500 randomly selected labeled examples (around 4K-10K km$^2$) we reach performance levels analogous to those achieved with the full labeled datasets (about 150K image chips or 3M km$^2$ in each area of interest - AOI) on all modalities, AOIs and downstream tasks. This leads us to think that the model has captured significant earth features useful in a wide variety of scenarios. To enhance our model's usability in practice, its architecture allows inference in contexts with missing modalities and even missing channels within each modality. Additionally, we visually show that this embedding space, obtained with no labels, is sensible to the different earth features represented by the labelled datasets we selected.

Joseph A. Gallego-Mejia, Anna Jungbluth, Laura Martínez-Ferrer et al.

Self-supervised learning (SSL) models have recently demonstrated remarkable performance across various tasks, including image segmentation. This study delves into the emergent characteristics of the Self-Distillation with No Labels (DINO) algorithm and its application to Synthetic Aperture Radar (SAR) imagery. We pre-train a vision transformer (ViT)-based DINO model using unlabeled SAR data, and later fine-tune the model to predict high-resolution land cover maps. We rigorously evaluate the utility of attention maps generated by the ViT backbone and compare them with the model's token embedding space. We observe a small improvement in model performance with pre-training compared to training from scratch and discuss the limitations and opportunities of SSL for remote sensing and land cover segmentation. Beyond small performance increases, we show that ViT attention maps hold great intrinsic value for remote sensing, and could provide useful inputs to other algorithms. With this, our work lays the groundwork for bigger and better SSL models for Earth Observation.

Laura Martínez-Ferrer, Anna Jungbluth, Joseph A. Gallego-Mejia et al.

In this work we pre-train a DINO-ViT based model using two Synthetic Aperture Radar datasets (S1GRD or GSSIC) across three regions (China, Conus, Europe). We fine-tune the models on smaller labeled datasets to predict vegetation percentage, and empirically study the connection between the embedding space of the models and their ability to generalize across diverse geographic regions and to unseen data. For S1GRD, embedding spaces of different regions are clearly separated, while GSSIC's overlaps. Positional patterns remain during fine-tuning, and greater distances in embeddings often result in higher errors for unfamiliar regions. With this, our work increases our understanding of generalizability for self-supervised models applied to remote sensing.

Matthew J Allen, Francisco Dorr, Joseph Alejandro Gallego Mejia et al.

Satellite-based remote sensing has revolutionised the way we address global challenges. Huge quantities of Earth Observation (EO) data are generated by satellite sensors daily, but processing these large datasets for use in ML pipelines is technically and computationally challenging. While some preprocessed Earth observation datasets exist, their content is often limited to optical or near-optical wavelength data, which is ineffective at night or in adverse weather conditions. Synthetic Aperture Radar (SAR), an active sensing technique based on microwave length radiation, offers a viable alternative. However, the application of machine learning to SAR has been limited due to a lack of ML-ready data and pipelines, particularly for the full diversity of SAR data, including polarimetry, coherence and interferometry. In this work, we introduce M3LEO, a multi-modal, multi-label Earth observation dataset that includes polarimetric, interferometric, and coherence SAR data derived from Sentinel-1, alongside multispectral Sentinel-2 imagery and auxiliary data describing terrain properties such as land use. M3LEO spans approximately 17M 4x4 km data chips from six diverse geographic regions. The dataset is complemented by a flexible PyTorch Lightning framework configured using Hydra to accommodate its use across diverse ML applications in Earth observation. We provide tools to process any dataset available on popular platforms such as Google Earth Engine for seamless integration with our framework. We show that the distribution shift in self-supervised embeddings is substantial across geographic regions, even when controlling for terrain properties. Data: huggingface.co/M3LEO, Code: github.com/spaceml-org/M3LEO.

Issam Laradji, Pau Rodriguez, Freddie Kalaitzis et al.

Cattle farming is responsible for 8.8\% of greenhouse gas emissions worldwide. In addition to the methane emitted due to their digestive process, the growing need for grazing areas is an important driver of deforestation. While some regulations are in place for preserving the Amazon against deforestation, these are being flouted in various ways, hence the need to scale and automate the monitoring of cattle ranching activities. Through a partnership with \textit{Global Witness}, we explore the feasibility of tracking and counting cattle at the continental scale from satellite imagery. With a license from Maxar Technologies, we obtained satellite imagery of the Amazon at 40cm resolution, and compiled a dataset of 903 images containing a total of 28498 cattle. Our experiments show promising results and highlight important directions for the next steps on both counting algorithms and the data collection process for solving such challenges. The code is available at \url{https://github.com/IssamLaradji/cownter_strike}.

Michael J. Smith, Luke Fleming, James E. Geach et al.

We present Dargana, a fine-tuned variant of the EarthPT time-series foundation model that achieves specialisation using <3% of its pre-training data volume and 5% of its pre-training compute. Dargana is fine-tuned to generate regularly updated classification of tree canopy cover at 10m resolution, distinguishing conifer and broadleaved tree types. Using Cornwall, UK, as a test case, the model achieves a pixel-level ROC-AUC of 0.98 and a PR-AUC of 0.83 on unseen satellite imagery. Dargana can identify fine structures like hedgerows and coppice below the training sample limit, and can track temporal changes to canopy cover such as new woodland establishment. Our results demonstrate how pre-trained Large Observation Models like EarthPT can be specialised for granular, dynamic land cover monitoring from space, providing a valuable, scalable tool for natural capital management and conservation.

Muhammed Razzak, Gonzalo Mateo-Garcia, Luis Gómez-Chova et al.

High resolution remote sensing imagery is used in broad range of tasks, including detection and classification of objects. High-resolution imagery is however expensive, while lower resolution imagery is often freely available and can be used by the public for range of social good applications. To that end, we curate a multi-spectral multi-image super-resolution dataset, using PlanetScope imagery from the SpaceNet 7 challenge as the high resolution reference and multiple Sentinel-2 revisits of the same imagery as the low-resolution imagery. We present the first results of applying multi-image super-resolution (MISR) to multi-spectral remote sensing imagery. We, additionally, introduce a radiometric consistency module into MISR model the to preserve the high radiometric resolution of the Sentinel-2 sensor. We show that MISR is superior to single-image super-resolution and other baselines on a range of image fidelity metrics. Furthermore, we conduct the first assessment of the utility of multi-image super-resolution on building delineation, showing that utilising multiple images results in better performance in these downstream tasks.

Christian Schroeder de Witt, Catherine Tong, Valentina Zantedeschi et al.

Extreme precipitation events, such as violent rainfall and hail storms, routinely ravage economies and livelihoods around the developing world. Climate change further aggravates this issue. Data-driven deep learning approaches could widen the access to accurate multi-day forecasts, to mitigate against such events. However, there is currently no benchmark dataset dedicated to the study of global precipitation forecasts. In this paper, we introduce \textbf{RainBench}, a new multi-modal benchmark dataset for data-driven precipitation forecasting. It includes simulated satellite data, a selection of relevant meteorological data from the ERA5 reanalysis product, and IMERG precipitation data. We also release \textbf{PyRain}, a library to process large precipitation datasets efficiently. We present an extensive analysis of our novel dataset and establish baseline results for two benchmark medium-range precipitation forecasting tasks. Finally, we discuss existing data-driven weather forecasting methodologies and suggest future research avenues.

Dolores Garcia, Gonzalo Mateo-Garcia, Hannes Bernhardt et al.

Where are the Earth's streams flowing right now? Inland surface waters expand with floods and contract with droughts, so there is no one map of our streams. Current satellite approaches are limited to monthly observations that map only the widest streams. These are fed by smaller tributaries that make up much of the dendritic surface network but whose flow is unobserved. A complete map of our daily waters can give us an early warning for where droughts are born: the receding tips of the flowing network. Mapping them over years can give us a map of impermanence of our waters, showing where to expect water, and where not to. To that end, we feed the latest high-res sensor data to multiple deep learning models in order to map these flowing networks every day, stacking the times series maps over many years. Specifically, i) we enhance water segmentation to $50$ cm/pixel resolution, a 60$\times$ improvement over previous state-of-the-art results. Our U-Net trained on 30-40cm WorldView3 images can detect streams as narrow as 1-3m (30-60$\times$ over SOTA). Our multi-sensor, multi-res variant, WasserNetz, fuses a multi-day window of 3m PlanetScope imagery with 1m LiDAR data, to detect streams 5-7m wide. Both U-Nets produce a water probability map at the pixel-level. ii) We integrate this water map over a DEM-derived synthetic valley network map to produce a snapshot of flow at the stream level. iii) We apply this pipeline, which we call Pix2Streams, to a 2-year daily PlanetScope time-series of three watersheds in the US to produce the first high-fidelity dynamic map of stream flow frequency. The end result is a new map that, if applied at the national scale, could fundamentally improve how we manage our water resources around the world.

Michel Deudon, Alfredo Kalaitzis, Israel Goytom et al.

Generative deep learning has sparked a new wave of Super-Resolution (SR) algorithms that enhance single images with impressive aesthetic results, albeit with imaginary details. Multi-frame Super-Resolution (MFSR) offers a more grounded approach to the ill-posed problem, by conditioning on multiple low-resolution views. This is important for satellite monitoring of human impact on the planet -- from deforestation, to human rights violations -- that depend on reliable imagery. To this end, we present HighRes-net, the first deep learning approach to MFSR that learns its sub-tasks in an end-to-end fashion: (i) co-registration, (ii) fusion, (iii) up-sampling, and (iv) registration-at-the-loss. Co-registration of low-resolution views is learned implicitly through a reference-frame channel, with no explicit registration mechanism. We learn a global fusion operator that is applied recursively on an arbitrary number of low-resolution pairs. We introduce a registered loss, by learning to align the SR output to a ground-truth through ShiftNet. We show that by learning deep representations of multiple views, we can super-resolve low-resolution signals and enhance Earth Observation data at scale. Our approach recently topped the European Space Agency's MFSR competition on real-world satellite imagery.

Anna Jungbluth, Xavier Gitiaux, Shane A. Maloney et al.

Breakthroughs in our understanding of physical phenomena have traditionally followed improvements in instrumentation. Studies of the magnetic field of the Sun, and its influence on the solar dynamo and space weather events, have benefited from improvements in resolution and measurement frequency of new instruments. However, in order to fully understand the solar cycle, high-quality data across time-scales longer than the typical lifespan of a solar instrument are required. At the moment, discrepancies between measurement surveys prevent the combined use of all available data. In this work, we show that machine learning can help bridge the gap between measurement surveys by learning to super-resolve low-resolution magnetic field images and translate between characteristics of contemporary instruments in orbit. We also introduce the notion of physics-based metrics and losses for super-resolution to preserve underlying physics and constrain the solution space of possible super-resolution outputs.

Xavier Gitiaux, Shane A. Maloney, Anna Jungbluth et al.

Machine learning techniques have been successfully applied to super-resolution tasks on natural images where visually pleasing results are sufficient. However in many scientific domains this is not adequate and estimations of errors and uncertainties are crucial. To address this issue we propose a Bayesian framework that decomposes uncertainties into epistemic and aleatoric uncertainties. We test the validity of our approach by super-resolving images of the Sun's magnetic field and by generating maps measuring the range of possible high resolution explanations compatible with a given low resolution magnetogram.

Kara Lamb, Garima Malhotra, Athanasios Vlontzos et al.

High energy particles originating from solar activity travel along the the Earth's magnetic field and interact with the atmosphere around the higher latitudes. These interactions often manifest as aurora in the form of visible light in the Earth's ionosphere. These interactions also result in irregularities in the electron density, which cause disruptions in the amplitude and phase of the radio signals from the Global Navigation Satellite Systems (GNSS), known as 'scintillation'. In this paper we use a multi-scale residual autoencoder (Res-AE) to show the correlation between specific dynamic structures of the aurora and the magnitude of the GNSS phase scintillations ($σ_φ$). Auroral images are encoded in a lower dimensional feature space using the Res-AE, which in turn are clustered with t-SNE and UMAP. Both methods produce similar clusters, and specific clusters demonstrate greater correlations with observed phase scintillations. Our results suggest that specific dynamic structures of auroras are highly correlated with GNSS phase scintillations.

Kara Lamb, Garima Malhotra, Athanasios Vlontzos et al.

A Global Navigation Satellite System (GNSS) uses a constellation of satellites around the earth for accurate navigation, timing, and positioning. Natural phenomena like space weather introduce irregularities in the Earth's ionosphere, disrupting the propagation of the radio signals that GNSS relies upon. Such disruptions affect both the amplitude and the phase of the propagated waves. No physics-based model currently exists to predict the time and location of these disruptions with sufficient accuracy and at relevant scales. In this paper, we focus on predicting the phase fluctuations of GNSS radio waves, known as phase scintillations. We propose a novel architecture and loss function to predict 1 hour in advance the magnitude of phase scintillations within a time window of plus-minus 5 minutes with state-of-the-art performance.

Laure Delisle, Alfredo Kalaitzis, Krzysztof Majewski et al.

We report the first, to the best of our knowledge, hand-in-hand collaboration between human rights activists and machine learners, leveraging crowd-sourcing to study online abuse against women on Twitter. On a technical front, we carefully curate an unbiased yet low-variance dataset of labeled tweets, analyze it to account for the variability of abuse perception, and establish baselines, preparing it for release to community research efforts. On a social impact front, this study provides the technical backbone for a media campaign aimed at raising public and deciders' awareness and elevating the standards expected from social media companies.

Alfredo Kalaitzis, Ricardo Silva

Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has gained popularity due to its modular parametrization of joint distributions. Among other properties, copulas provide a recipe for combining flexible models for univariate marginal distributions with parametric families suitable for potentially high dimensional dependence structures. More radically, the extended rank likelihood approach of Hoff (2007) bypasses learning marginal models completely when such information is ancillary to the learning task at hand as in, e.g., standard dimensionality reduction problems or copula parameter estimation. The main idea is to represent data by their observable rank statistics, ignoring any other information from the marginals. Inference is typically done in a Bayesian framework with Gaussian copulas, and it is complicated by the fact this implies sampling within a space where the number of constraints increases quadratically with the number of data points. The result is slow mixing when using off-the-shelf Gibbs sampling. We present an efficient algorithm based on recent advances on constrained Hamiltonian Markov chain Monte Carlo that is simple to implement and does not require paying for a quadratic cost in sample size.

Alfredo Kalaitzis, Neil Lawrence

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data variance is already partially explained by other actors, for example sparse conditional dependencies between the covariates, or temporal correlations leaving some residual variance. We decompose the residual variance into its components through a generalised eigenvalue problem, which we call residual component analysis (RCA). We explore a range of new algorithms that arise from the framework, including one that factorises the covariance of a Gaussian density into a low-rank and a sparse-inverse component. We illustrate the ideas on the recovery of a protein-signaling network, a gene expression time-series data set and the recovery of the human skeleton from motion capture 3-D cloud data.