Gaussian splatting enables fast novel view synthesis in static 3D environments. However, reconstructing real-world environments remains challenging as distractors or occluders break the multi-view consistency assumption required for accurate 3D reconstruction. Most existing methods rely on external semantic information from pre-trained models, introducing additional computational overhead as pre-processing steps or during optimization. In this work, we propose a novel method, DeSplat, that directly separates distractors and static scene elements purely based on volume rendering of Gaussian primitives. We initialize Gaussians within each camera view for reconstructing the view-specific dis-tractors to separately model the static 3D scene and dis-tractors in the alpha compositing stages. DeSplat yields an explicit scene separation of static elements and distrac-tors, achieving comparable results to prior distractor-free approaches without sacrificing rendering speed. We demonstrate DeSplat’s effectiveness on three benchmark data sets for distractor-free novel view synthesis. See the project website at https://aaltoml.github.io/desplat/.

Graph diffusion models, dominant in graph generative modeling, remain underexplored for graph-to-graph translation tasks like chemical reaction prediction. We demonstrate that standard permutation equivariant denoisers face fundamental limitations in these tasks due to their inability to break symmetries in noisy inputs. To address this, we propose \emph{aligning} input and target graphs to break input symmetries while preserving permutation equivariance in non-matching graph portions. Using retrosynthesis (i.e., the task of predicting precursors for synthesis of a given target molecule) as our application domain, we show how alignment dramatically improves discrete diffusion model performance from $5$\% to a SOTA-matching $54.7$\% top-1 accuracy. Code is available at https://github.com/Aalto-QuML/DiffAlign.

The rising interest in Bayesian deep learning (BDL) has led to a plethora of methods for estimating the posterior distribution. However, efficient computation of inferences, such as predictions, has been largely overlooked with Monte Carlo integration remaining the standard. In this work we examine streamlining prediction in BDL through a single forward pass without sampling. For this, we use local linearisation of activation functions and local Gaussian approximations at linear layers. Thus allowing us to analytically compute an approximation of the posterior predictive distribution. We showcase our approach for both MLP and transformers, such as ViT and GPT-2, and assess its performance on regression and classification tasks. Open-source library: https://github.com/AaltoML/SUQ.

The covariance for clean data given a noisy observation is an important quantity in many training-free guided generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked to the covariance through the second-order Tweedie's formula. We integrate these sources of information using (i) a novel method to transfer covariance estimates across noise levels and (ii) low-rank updates in a given noise level. We validate the method on linear inverse problems, where it outperforms recent baselines, especially with fewer diffusion steps.

In reinforcement learning (RL), world models serve as internal simulators, enabling agents to predict environment dynamics and future outcomes in order to make informed decisions. While previous approaches leveraging discrete latent spaces, such as DreamerV3, have demonstrated strong performance in discrete action settings and visual control tasks, their comparative performance in state-based continuous control remains underexplored. In contrast, methods with continuous latent spaces, such as TD-MPC2, have shown notable success in state-based continuous control benchmarks. In this paper, we demonstrate that modeling discrete latent states has benefits over continuous latent states and that discrete codebook encodings are more effective representations for continuous control, compared to alternative encodings, such as one-hot and label-based encodings. Based on these insights, we introduce DCWM: Discrete Codebook World Model, a self-supervised world model with a discrete and stochastic latent space, where latent states are codes from a codebook. We combine DCWM with decision-time planning to get our model-based RL algorithm, named DC-MPC: Discrete Codebook Model Predictive Control, which performs competitively against recent state-of-the-art algorithms, including TD-MPC2 and DreamerV3, on continuous control benchmarks.

Recent research has focused on designing neural samplers that amortize the process of sampling from unnormalized densities. However, despite significant advancements, they still fall short of the state-of-the-art MCMC approach, Parallel Tempering (PT), when it comes to the efficiency of target evaluations. On the other hand, unlike a well-trained neural sampler, PT yields only dependent samples and needs to be rerun---at considerable computational cost---whenever new samples are required. To address these weaknesses, we propose the Progressive Tempering Sampler with Diffusion (PTSD), which trains diffusion models sequentially across temperatures, leveraging the advantages of PT to improve the training of neural samplers. We also introduce a novel method to combine high-temperature diffusion models to generate approximate lower-temperature samples, which are minimally refined using MCMC and used to train the next diffusion model. PTSD enables efficient reuse of sample information across temperature levels while generating well-mixed, uncorrelated samples. Our method significantly improves target evaluation efficiency, outperforming diffusion-based neural samplers.

The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these representations, effectively enabling us to learn a continuous distribution using discrete parameters. We consider both 2D densities and quantized neural networks, where we introduce a tractable learning approach using probabilistic circuits. This method offers a scalable solution to manage complex distributions and provides clear insights into model behavior. We validate our approach with various models, demonstrating inference efficiency without sacrificing accuracy. This work advances scalable, interpretable machine learning by utilizing discrete approximations for probabilistic computations.

Deployment of deep neural networks in real-world settings typically requires adaptation to new tasks with few examples. Few-shot classification (FSC) provides a solution to this problem by leveraging pre-trained backbones for fast adaptation to new classes. However, approaches for multi-domain FSC typically result in complex pipelines aimed at information fusion and task-specific adaptation without consideration of the importance of backbone training. In this work, we introduce an effective strategy for backbone training and selection in multi-domain FSC by utilizing flatness-aware training and fine-tuning. Our work is theoretically grounded and empirically performs on par or better than state-of-the-art methods despite being simpler. Further, our results indicate that backbone training is crucial for good generalisation in FSC across different adaptation methods.

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with latent processes endowed with a non-linear diffusion process prior are intractable problems. We build upon work within variational inference, approximating the posterior process as a linear diffusion process, and point out pathologies in the approach. We propose an alternative parameterization of the Gaussian variational process using a site-based exponential family description. This allows us to trade a slow inference algorithm with fixed-point iterations for a fast algorithm for convex optimization akin to natural gradient descent, which also provides a better objective for learning model parameters.

Learning dynamical systems from sparse observations is critical in numerous fields, including biology, finance, and physics. Even if tackling such problems is standard in general information fusion, it remains challenging for contemporary machine learning models, such as diffusion models. We introduce a method that integrates conditional particle filtering with ancestral sampling and diffusion models, enabling the generation of realistic trajectories that align with observed data. Our approach uses a smoother based on iterating a conditional particle filter with ancestral sampling to first generate plausible trajectories matching observed marginals, and learns the corresponding diffusion model. This approach provides both a generative method for high-quality, smoothed trajectories under complex constraints, and an efficient approximation of the particle smoothing distribution for classical tracking problems. We demonstrate the approach in time-series generation and interpolation tasks, including vehicle tracking and single-cell RNA sequencing data.

Mixture models are traditionally represented and learned by adding several distributions as components. Allowing mixtures to subtract probability mass or density can drastically reduce the number of components needed to model complex distributions. However, learning such subtractive mixtures while ensuring they still encode a non-negative function is challenging. We investigate how to learn and perform inference on deep subtractive mixtures by squaring them. We do this in the framework of probabilistic circuits, which enable us to represent tensorized mixtures and generalize several other subtractive models. We theoretically prove that the class of squared circuits allowing subtractions can be exponentially more expressive than traditional additive mixtures; and, we empirically show this increased expressiveness on a series of real-world distribution estimation tasks.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (*i*) a way to scale function-space methods to large data sets via sparsification, (*ii*) retention of prior knowledge when access to past data is limited, and (*iii*) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.

Dynamic neural networks are a recent technique that promises a remedy for the increasing size of modern deep learning models by dynamically adapting their computational cost to the difficulty of the inputs. In this way, the model can adjust to a limited computational budget. However, the poor quality of uncertainty estimates in deep learning models makes it difficult to distinguish between hard and easy samples. To address this challenge, we present a computationally efficient approach for post-hoc uncertainty quantification in dynamic neural networks. We show that adequately quantifying and accounting for both aleatoric and epistemic uncertainty through a probabilistic treatment of the last layers improves the predictive performance and aids decision-making when determining the computational budget. In the experiments, we show improvements on CIFAR100, ImageNet, and Caltech-256 in terms of accuracy, capturing uncertainty, and calibration error.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI’s lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Mixup is a popular data augmentation technique for training deep neural networks where additional samples are generated by linearly interpolating pairs of inputs and their labels. This technique is known to improve the generalization performance in many learning paradigms and applications. In this work, we first analyze Mixup and show that it implicitly regularizes infinitely many directional derivatives of all orders. Based on this new insight, we propose an improved version of Mixup, theoretically justified to deliver better generalization performance than the vanilla Mixup. To demonstrate the effectiveness of the proposed method, we conduct experiments across various domains such as images, tabular data, speech, and graphs. Our results show that the proposed method improves Mixup across multiple datasets using a variety of architectures, for instance, exhibiting an improvement over Mixup by 0.8% in ImageNet top-1 accuracy.

We introduce visual hints expansion for guiding stereo matching to improve generalization. Our work is motivated by the robustness of Visual Inertial Odometry (VIO) in computer vision and robotics, where a sparse and unevenly distributed set of feature points characterizes a scene. To improve stereo matching, we propose to elevate 2D hints to 3D points. These sparse and unevenly distributed 3D visual hints are expanded using a 3D random geometric graph, which enhances the learning and inference process. We evaluate our proposal on multiple widely adopted benchmarks and show improved performance without access to additional sensors other than the image sequence. To highlight practical applicability and symbiosis with visual odometry, we demonstrate how our methods run on embedded hardware.

We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint explicitly casts inference algorithms under the framework of numerical optimisation. We show that common approximations to Newton's method from the optimisation literature, namely Gauss-Newton and quasi-Newton methods (e.g., the BFGS algorithm), are still valid under this 'Bayes-Newton' framework. This leads to a suite of novel algorithms which are guaranteed to result in positive semi-definite (PSD) covariance matrices, unlike standard VI and EP. Our unifying viewpoint provides new insights into the connections between various inference schemes. All the presented methods apply to any model with a Gaussian prior and non-conjugate likelihood, which we demonstrate with (sparse) Gaussian processes and state space models.

Gaussian processes (GPs) provide a principled and direct approach for inference and learning on graphs. However, the lack of justified graph kernels for spatio-temporal modelling has held back their use in graph problems. We leverage an explicit link between stochastic partial differential equations (SPDEs) and GPs on graphs, introduce a framework for deriving graph kernels via SPDEs, and derive non-separable spatio-temporal graph kernels that capture interaction across space and time. We formulate the graph kernels for the stochastic heat equation and wave equation. We show that by providing novel tools for spatio-temporal GP modelling on graphs, we outperform pre-existing graph kernels in real-world applications that feature diffusion, oscillation, and other complicated interactions.

We present HybVIO, a novel hybrid approach for combining filtering-based visual-inertial odometry (VIO) with optimization-based SLAM. The core of our method is highly robust, independent VIO with improved IMU bias modeling, outlier rejection, stationarity detection, and feature track selection, which is adjustable to run on embedded hardware. Long-term consistency is achieved with a loosely-coupled SLAM module. In academic benchmarks, our solution yields excellent performance in all categories, especially in the real-time use case, where we outperform the current state-of-the-art. We also demonstrate the feasibility of VIO for vehicular tracking on consumer-grade hardware using a custom dataset, and show good performance in comparison to current commercial VISLAM alternatives.

We introduce Interpolation Consistency Training (ICT), a simple and computation efficient algorithm for training Deep Neural Networks in the semi-supervised learning paradigm. ICT encourages the prediction at an interpolation of unlabeled points to be consistent with the interpolation of the predictions at those points. In classification problems, ICT moves the decision boundary to low-density regions of the data distribution. Our experiments show that ICT achieves state-of-the-art performance when applied to standard neural network architectures on the CIFAR-10 and SVHN benchmark datasets. Our theoretical analysis shows that ICT corresponds to a certain type of data-adaptive regularization with unlabeled points which reduces overfitting to labeled points under high confidence values.

Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient Kalman filter-like recursions, resulting in algorithms whose computational and memory requirements scale linearly in the number of inducing points, whilst also enabling parallel parameter updates and stochastic optimisation. Under this paradigm, we derive a general site-based approach to approximate inference, whereby we approximate the non-Gaussian likelihood with local Gaussian terms, called sites. Our approach results in a suite of novel sparse extensions to algorithms from both the machine learning and signal processing literature, including variational inference, expectation propagation, and the classical nonlinear Kalman smoothers. The derived methods are suited to large time series, and we also demonstrate their applicability to spatio-temporal data, where the model has separate inducing points in both time and space.

Sparse variational Gaussian process (SVGP) methods are a common choice for non-conjugate Gaussian process inference because of their computational benefits. In this paper, we improve their computational efficiency by using a dual parameterization where each data example is assigned dual parameters, similarly to site parameters used in expectation propagation. Our dual parameterization speeds-up inference using natural gradient descent, and provides a tighter evidence lower bound for hyperparameter learning. The approach has the same memory cost as the current SVGP methods, but it is faster and more accurate.

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with respect to time. Our natural gradient approach enables application of parallel filtering and smoothing, further reducing the temporal span complexity to be logarithmic in the number of time steps. We derive a sparse approximation that constructs a state-space model over a reduced set of spatial inducing points, and show that for separable Markov kernels the full and sparse cases exactly recover the standard variational GP, whilst exhibiting favourable computational properties. To further improve the spatial scaling we propose a mean-field assumption of independence between spatial locations which, when coupled with sparsity and parallelisation, leads to an efficient and accurate method for large spatio-temporal problems.

Neural network models are known to reinforce hidden data biases, making them unreliable and difficult to interpret. We seek to build models that `know what they do not know' by introducing inductive biases in the function space. We show that periodic activation functions in Bayesian neural networks establish a connection between the prior on the network weights and translation-invariant, stationary Gaussian process priors. Furthermore, we show that this link goes beyond sinusoidal (Fourier) activations by also covering triangular wave and periodic ReLU activation functions. In a series of experiments, we show that periodic activation functions obtain comparable performance for in-domain data and capture sensitivity to perturbed inputs in deep neural networks for out-of-domain detection.

Simulation-based techniques such as variants of stochastic Runge–Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and non-parametric models, and neural SDEs. Stochastic Runge–Kutta relies on the use of sampling schemes that can be inefficient in high dimensions. We address this issue by revisiting the classical SDE literature and derive direct approximations to the (typically intractable) Fokker–Planck–Kolmogorov equation by matching moments. We show how this workflow is fast, scales to high-dimensional latent spaces, and is applicable to scarce-data applications, where a non-parametric SDE with a driving Gaussian process velocity field specifies the model.

Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support large numbers of off-the-grid spatial data-points and long time-series which is a hallmark of many applications. Pseudo-point approximations, one of the gold-standard methods for scaling GPs to large data sets, are well suited for handling off-the-grid spatial data. However, they cannot handle long temporal observation horizons effectively reverting to cubic computational scaling in the time dimension. State space GP approximations are well suited to handling temporal data, if the temporal GP prior admits a Markov form, leading to linear complexity in the number of temporal observations, but have a cubic spatial cost and cannot handle off-the-grid spatial data. In this work we show that there is a simple and elegant way to combine pseudo-point methods with the state space GP approximation framework to get the best of both worlds. The approach hinges on a surprising conditional independence property which applies to space–time separable GPs. We demonstrate empirically that the combined approach is more scalable and applicable to a greater range of spatio-temporal problems than either method on its own.

We introduce a principled approach for synthesizing new views of a scene given a single source image. Previous methods for novel view synthesis can be divided into image-based rendering methods (e.g., flow prediction) or pixel generation methods. Flow predictions enable the target view to re-use pixels directly, but can easily lead to distorted results. Directly regressing pixels can produce structurally consistent results but generally suffer from the lack of low-level details. In this paper, we utilize an encoder-decoder architecture to regress pixels of a target view. In order to maintain details, we couple the decoder aligned feature maps with skip connections, where the alignment is guided by predicted depth map of the target view. Our experimental results show that our method does not suffer from distortions and successfully preserves texture details with aligned skip connections.

Robust and accurate six degree-of-freedom tracking on portable devices remains a challenging problem, especially on small hand-held devices such as smartphones. For improved robustness and accuracy, complementary movement information from an IMU and a camera is often fused. Conventional visual-inertial methods fuse information from IMUs with a sparse cloud of feature points tracked by the device camera. We consider a visually dense approach, where the IMU data is fused with the dense optical flow field estimated from the camera data. Learning-based methods applied to the full image frames can leverage visual cues and global consistency of the flow field to improve the flow estimates. We show how a learning-based optical flow model can be combined with conventional inertial navigation, and how ideas from probabilistic deep learning can aid the robustness of the measurement updates. The practical applicability is demonstrated on real-world data acquired by an iPad in a challenging low-texture environment.

Multi-output Gaussian processes (MOGPs) leverage the flexibility and interpretability of GPs while capturing structure across outputs, which is desirable, for example, in spatio-temporal modelling. The key problem with MOGPs is their computational scaling $O(n^3 p^3)$, which is cubic in the number of both inputs $n$ (e.g., time points or locations) and outputs $p$. For this reason, a popular class of MOGPs assumes that the data live around a low-dimensional linear subspace, reducing the complexity to $O(n^3 m^3)$. However, this cost is still cubic in the dimensionality of the subspace $m$, which is still prohibitively expensive for many applications. We propose the use of a sufficient statistic of the data to accelerate inference and learning in MOGPs with orthogonal bases. The method achieves linear scaling in $m$ in practice, allowing these models to scale to large $m$ without sacrificing significant expressivity or requiring approximation. This advance opens up a wide range of real-world tasks and can be combined with existing GP approximations in a plug-and-play way. We demonstrate the efficacy of the method on various synthetic and real-world data sets.

We formulate approximate Bayesian inference in non-conjugate temporal and spatio-temporal Gaussian process models as a simple parameter update rule applied during Kalman smoothing. This viewpoint encompasses most inference schemes, including expectation propagation (EP), the classical (Extended, Unscented, etc.) Kalman smoothers, and variational inference. We provide a unifying perspective on these algorithms, showing how replacing the power EP moment matching step with linearisation recovers the classical smoothers. EP provides some benefits over the traditional methods via introduction of the so-called cavity distribution, and we combine these benefits with the computational efficiency of linearisation, providing extensive empirical analysis demonstrating the efficacy of various algorithms under this unifying framework. We provide a fast implementation of all methods in JAX.

We propose a method for fusing stereo disparity estimation with movement-induced prior information. Instead of independent inference frame-by-frame, we formulate the problem as a non-parametric learning task in terms of a temporal Gaussian process prior with a movement-driven kernel for inter-frame reasoning. We present a hierarchy of three Gaussian process kernels depending on the availability of motion information, where our main focus is on a new gyroscope-driven kernel for handheld devices with low-quality MEMS sensors, thus also relaxing the requirement of having full 6D camera poses available. We show how our method can be combined with two state-of-the-art deep stereo methods. The method either work in a plug-and-play fashion with pre-trained deep stereo networks, or further improved by jointly training the kernels together with encoder-decoder architectures, leading to consistent improvement.

We introduce a new category of generative autoencoders called automodulators. These networks can faithfully reproduce individual real-world input images like regular autoencoders, but also generate a fused sample from an arbitrary combination of several such images, allowing instantaneous "style-mixing" and other new applications. An automodulator decouples the data flow of decoder operations from statistical properties thereof and uses the latent vector to modulate the former by the latter, with a principled approach for mutual disentanglement of decoder layers. Prior work has explored similar decoder architecture with GANs, but their focus has been on random sampling. A corresponding autoencoder could operate on real input images. For the first time, we show how to train such a general-purpose model with sharp outputs in high resolution, using novel training techniques, demonstrated on four image data sets. Besides style-mixing, we show state-of-the-art results in autoencoder comparison, and visual image quality nearly indistinguishable from state-of-the-art GANs. We expect the automodulator variants to become a useful building block for image applications and other data domains.

We introduce a new family of non-linear neural network activation functions that mimic the properties induced by the widely-used Mat\'ern family of kernels in Gaussian process (GP) models. This class spans a range of locally stationary models of various degrees of mean-square differentiability. We show an explicit link to the corresponding GP models in the case that the network consists of one infinitely wide hidden layer. In the limit of infinite smoothness the Mat\'ern family results in the RBF kernel, and in this case we recover RBF activations. Mat\'ern activation functions result in similar appealing properties to their counterparts in GP models, and we demonstrate that the local stationarity property together with limited mean-square differentiability shows both good performance and uncertainty calibration in Bayesian deep learning tasks. In particular, local stationarity helps calibrate out-of-distribution (OOD) uncertainty. We demonstrate these properties on classification and regression benchmarks and a radar emitter classification task.

We present a generative autoencoder that provides fast encoding, faithful reconstructions (e.g. retaining the identity of a face), sharp generated/reconstructed samples in high resolutions, and a well-structured latent space that supports semantic manipulation of the inputs. There are no current autoencoder or GAN models that satisfactorily achieve all of these. We build on the progressively growing autoencoder model PIONEER , for which we completely alter the training dynamics based on a careful analysis of recently introduced normalization schemes. We show significantly improved visual and quantitative results for face identity conservation in CELEBA-HQ. Our model achieves state-of-the-art disentanglement of latent space, both quantitatively and via realistic image attribute manipulations. On the LSUN Bedrooms dataset, we improve the disentanglement performance of the vanilla PIONEER, despite having a simpler model. Overall, our results indicate that the PIONEER networks provide a way towards photorealistic face manipulation.

Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in the domain of interest, which both constrains the GP and attains a low-rank representation that is used for speeding up inference. The method scales as O(nm^2) in prediction and O(m^3) in hyperparameter learning for regression, where n is the number of data points and m the number of features. Furthermore, we make use of the variational approach to allow the method to deal with non-Gaussian likelihoods. The experiments cover both simulated and empirical data in which the boundary conditions allow for inclusion of additional physical information.

In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal’s amplitude and phase information, making time domain resynthesis straightforward. However, these models are still not widely used since they come at a high computational cost, and because they are formulated in such a way that it can be difficult to interpret all the modelling assumptions. By showing their equivalence to Spectral Mixture Gaussian processes, we illuminate the underlying model assumptions and provide a general framework for constructing more complex models that better approximate real-world signals. Our interpretation makes it intuitive to inspect, compare, and alter the models since all prior knowledge is encoded in the Gaussian process kernel functions. We utilise a state space representation to perform efficient inference via Kalman smoothing, and we demonstrate how our interpretation allows for efficient parameter learning in the frequency domain.

We propose a novel idea for depth estimation from multi-view image-pose pairs, where the model has capability to leverage information from previous latent-space encodings of the scene. This model uses pairs of images and poses, which are passed through an encoder-decoder model for disparity estimation. The novelty lies in soft-constraining the bottleneck layer by a nonparametric Gaussian process prior. We propose a pose-kernel structure that encourages similar poses to have resembling latent spaces. The flexibility of the Gaussian process (GP) prior provides adapting memory for fusing information from nearby views. We train the encoder-decoder and the GP hyperparameters jointly end-to-end. In addition to a batch method, we derive a lightweight estimation scheme that circumvents standard pitfalls in scaling Gaussian process inference, and demonstrate how our scheme can run in real-time on smart devices.

A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and nonnegative matrix factorisation can be jointly formulated as a spectral mixture Gaussian process model with nonstationary priors over the amplitude variance parameters. Further, we formulate this nonlinear model’s state space representation, making it amenable to infinite-horizon Gaussian process regression with approximate inference via expectation propagation, which scales linearly in the number of time steps and quadratically in the state dimensionality. By doing so, we are able to process audio signals with hundreds of thousands of data points. We demonstrate, on various tasks with empirical data, how this inference scheme outperforms more standard techniques that rely on extended Kalman filtering.

We present a method for scalable and fully 3D magnetic field simultaneous localisation and mapping (SLAM) using local anomalies in the magnetic field as a source of position information. These anomalies are due to the presence of ferromagnetic material in the structure of buildings and in objects such as furniture. We represent the magnetic field map using a Gaussian process model and take well-known physical properties of the magnetic field into account. We build local maps using three-dimensional hexagonal block tiling. To make our approach computationally tractable we use reduced-rank Gaussian process regression in combination with a Rao-Blackwellised particle filter. We show that it is possible to obtain accurate position and orientation estimates using measurements from a smartphone, and that our approach provides a scalable magnetic field SLAM algorithm in terms of both computational complexity and map storage.

Camera calibration for estimating the intrinsic parameters and lens distortion is a prerequisite for various monocular vision applications including feature tracking and video stabilization. This application paper proposes a model for estimating the parameters on the fly by fusing gyroscope and camera data, both readily available in modern day smartphones. The model is based on joint estimation of visual feature positions, camera parameters, and the camera pose, the movement of which is assumed to follow the movement predicted by the gyroscope. Our model assumes the camera movement to be free, but continuous and differentiable, and individual features are assumed to stay stationary. The estimation is performed online using an extended Kalman filter, and it is shown to outperform existing methods in robustness and insensitivity to initialization. We demonstrate the method using simulated data and empirical data from an iPad.

Building a complete inertial navigation system using the limited quality data provided by current smartphones has been regarded challenging, if not impossible. This paper shows that by careful crafting and accounting for the weak information in the sensor samples, smartphones are capable of pure inertial navigation. We present a probabilistic approach for orientation and use-case free inertial odometry, which is based on double-integrating rotated accelerations. The strength of the model is in learning additive and multiplicative IMU biases online. We are able to track the phone position, velocity, and pose in realtime and in a computationally lightweight fashion by solving the inference with an extended Kalman filter. The information fusion is completed with zero-velocity updates (if the phone remains stationary), altitude correction from barometric pressure readings (if available), and pseudo-updates constraining the momentary speed. We demonstrate our approach using an iPad and iPhone in several indoor dead-reckoning applications and in a measurement tool setup.

We provide a comprehensive overview and tooling for GP modelling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensonal GP models in O(n) time and memory complexity. While existing literature has focused on the connection between GP regression and state space methods, the computational primitives allowing for inference using general likelihoods in combination with the Laplace approximation (LA), variational Bayes (VB), and assumed density filtering (ADF) / expectation propagation (EP) schemes has been largely overlooked. We present means of combining the efficient O(n) state space methodology with existing inference methods. We also furher extend existing methods, and provide unifying code implementing all approaches.

Gaussian processes provide a flexible framework for forecasting, removing noise, and interpreting long temporal datasets. State space modelling (Kalman filtering) enables these non-parametric models to be deployed on long datasets by reducing the complexity to linear in the number of data points. The complexity is still cubic in the state dimension m which is an impediment to practical application. In certain special cases (Gaussian likelihood, regular spacing) the GP posterior will reach a steady posterior state when the data are very long. We leverage this and formulate an inference scheme for GPs with general likelihoods, where inference is based on single-sweep EP (assumed density filtering). The infinite-horizon model tackles the cubic cost in the state dimensionality and reduces the cost in the state dimension m to O(m^2) per data point. The model is extended to online-learning of hyperparameters. We show examples for large finite-length modelling problems, and present how the method runs in real-time on a smartphone on a continuous data stream updated at 100 Hz.

This paper presents a novel method for visual-inertial odometry. The method is based on an information fusion framework employing low-cost IMU sensors and the monocular camera in a standard smartphone. We formulate a sequential inference scheme, where the IMU drives the dynamical model and the camera frames are used in coupling trailing sequences of augmented poses. The novelty in the model is in taking into account all the cross-terms in the updates, thus propagating the inter-connected uncertainties throughout the model. Stronger coupling between the inertial and visual data sources leads to robustness against occlusion and feature-poor environments. We demonstrate results on data collected with an iPhone and provide comparisons against the Tango device and using the EuRoC data set.

Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography, genetics, and computational social science. These networks are typically constructed by hand through a very time-consuming process, which requires comparing large numbers of historical records manually. We develop computational methods for automatically inferring large-scale genealogical networks. A comparison with human-constructed networks attests to the accuracy of the proposed methods. To demonstrate the applicability of the inferred large-scale genealogical networks, we present a longitudinal analysis on the mating patterns observed in a network. This analysis shows a consistent tendency of people choosing a spouse with a similar socioeconomic status, a phenomenon known as assortative mating. Interestingly, we do not observe this tendency to consistently decrease (nor increase) over our study period of 150 years.

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian nonparametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior to the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications. We demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally efficient and yet allows for a fully Bayesian treatment of the problem. Compared to conventional system identification tools or existing learning methods, we show competitive performance and reliable quantification of uncertainties in the model.

The added flexibility of Student-t processes (TPs) over Gaussian processes (GPs) robustifies inference in outlier-contaminated noisy data. The uncertainties are better accounted for than in GP regression, because the predictive covariances explicitly depend on the training observations. For an entangled noise model, the canonical-form TP regression problem can be solved analytically, but the naive TP and GP solutions share the same cubic computational cost in the number of training observations. We show how a large class of temporal TP regression models can be reformulated as state space models, and how a forward filtering and backward smoothing recursion can be derived for solving the inference analytically in linear time complexity. This is a novel finding that generalizes the previously known connection between Gaussian process regression and Kalman filtering to more general elliptical processes and non-Gaussian Bayesian filtering. We derive this connection, demonstrate the benefits of the approach with examples, and finally apply the method to empirical data.

This paper shows how periodic covariance functions in Gaussian process regression can be reformulated as state space models, which can be solved with classical Kalman filtering theory. This reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into linear time complexity. The representation is based on expanding periodic covariance functions into a series of stochastic resonators. The explicit representation of the canonical periodic covariance function is written out and the expansion is shown to uniformly converge to the exact covariance function with a known convergence rate. The framework is generalized to quasi-periodic covariance functions by introducing damping terms in the system and applied to two sets of real data. The approach could be easily extended to non-stationary and spatio-temporal variants.