Lifelong place recognition is an essential and challenging task in computer vision with vast applications robust localization efficient large-scale 3D reconstruction. Progress currently hindered by a lack of large, diverse, publicly available datasets. We contribute Mapillary Street-Level Sequences (SLS), large dataset for urban suburban from image sequences. It contains more than 1.6 million images curated the collaborative mapping platform. The orders magnitude larger current data sources,...

How we choose to represent our data has a fundamental impact on ability subsequently extract information from them. Machine learning promises automatically determine efficient representations large unstructured datasets, such as those arising in biology. However, empirical evidence suggests that seemingly minor changes these machine models yield drastically different result biological interpretations of data. This begs the question what even constitutes most meaningful representation. Here,...

We consider kernel methods on general geodesic metric spaces and provide both negative positive results. First we show that the common Gaussian can only be generalized to a definite space if is flat. As result, for data Riemannian manifold, manifold Euclidean. This implies any attempt design kernels curved manifolds futile. However, with conditionally distances Laplacian while retaining definiteness. some spaces, including spheres hyperbolic spaces. Our theoretical results are verified empirically.

As the collection of large datasets becomes increasingly automated, occurrence outliers will increase -- "big data" implies outliers". While principal component analysis (PCA) is often used to reduce size data, and scalable solutions exist, it well-known that can arbitrarily corrupt results. Unfortunately, state-of-the-art approaches for robust PCA do not scale beyond small-to-medium sized datasets. To address this, we introduce Grassmann Average (GA), which expresses dimensionality...

Deep generative models provide a systematic way to learn nonlinear data distributions, through set of latent variables and "generator" function that maps points into the input space. The nonlinearity generator imply space gives distorted view Under mild conditions, we show this distortion can be characterized by stochastic Riemannian metric, demonstrate distances interpolants are significantly improved under metric. This in turn improves probability sampling algorithms clustering Our...

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original data; e.g.~new images are formed rotating old ones. Current schemes, however, rely on manual specification of applied transformations, making data an implicit form feature engineering. With eye towards true end-to-end learning, we suggest learning per-class basis. Particularly, align image pairs within each class...

Triple-negative breast cancer (TNBC) is an aggressive and difficult-to-treat type that represents approximately 15% of all cancers. Recently, stromal tumor-infiltrating lymphocytes (sTIL) resurfaced as a strong prognostic biomarker for overall survival (OS) TNBC patients. Manual assessment has innate limitations hinder clinical adoption, the International Immuno-Oncology Biomarker Working Group (TIL-WG) therefore envisioned computational sTIL could overcome these recommended any algorithm...

Racial bias in medicine, particularly dermatology, presents significant ethical and clinical challenges. It often results from the underrepresentation of darker skin tones training datasets for machine learning models. While efforts to address dermatology have focused on improving dataset diversity mitigating disparities discriminative models, impact racial generative models remains underexplored. Generative such as Variational Autoencoders (VAEs), are increasingly used healthcare...

Estimating means on Riemannian manifolds is generally computationally expensive because the distance function not known in closed-form for most manifolds. To overcome this, we show that diffusion can be efficiently estimated using score matching with gradient of Brownian motion transition densities same principle as models. Empirically, this more efficient than Monte Carlo simulation while retaining accuracy and also applicable to learned Our method, furthermore, extends computing Fr\'echet...

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these models familiar-looking, they restricted the inflexibility of geodesics, and rely on constructions which optimal only in domains. We consider extensions Principal Component Analysis (PCA) manifolds. Classic approaches seek a curve passing through mean that optimizes criteria interest. The requirements solution both is must pass tend imply methods work...

Spatial Transformer layers allow neural networks, at least in principle, to be invariant large spatial transformations image data. The model has, however, seen limited uptake as most practical implementations support only that are too restricted, e.g. affine or homographic maps, and/or destructive such thin plate splines. We investigate the use of flexible diffeomorphic within networks and demonstrate significant performance gains can attained over currently-used models. learned found both...

Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings studied phenomena. Unfortunately, these are not statistically identifiable, meaning they cannot be uniquely determined. Domain experts, therefore, need to tread carefully when interpreting these. Current solutions limit lack identifiability through additional constraints on model, e.g. by requiring labeled training data, or restricting expressivity model. We change goal: instead...

We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns joint Gaussian process posterior over solution. Such methods have concrete in statistics on Riemannian manifolds, where non-analytic ordinary differential equations are involved virtually all computations. The formulation permits marginalising uncertainty such less sensitive to inaccuracies. This leads new algorithms mean computations principal geodesic analysis....

We propose novel finite-dimensional spaces of well-behaved <inline-formula><tex-math notation="LaTeX">$\mathbb {R}^n\rightarrow \mathbb {R}^n$</tex-math></inline-formula> transformations. The latter are obtained by (fast and highly-accurate) integration continuous piecewise-affine velocity fields. proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), supports convenient modeling choices such as...

Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods estimating uncertainties are poorly calibrated, computationally expensive, or based on heuristics. We present new method that views embeddings as stochastic features rather than deterministic features. Our two main contributions (1) likelihood matches the triplet constraint evaluates probability of an anchor being closer to positive...

In large datasets, manual data verification is impossible, and we must expect the number of outliers to increase with size. While principal component analysis (PCA) can reduce size, scalable solutions exist, it well-known that arbitrarily corrupt results. Unfortunately, state-of-the-art approaches for robust PCA are not scalable. We note in a zero-mean dataset, each observation spans one-dimensional subspace, giving point on Grassmann manifold. show average subspace corresponds leading...