Markovian Gaussian Process Variational Autoencoders

Deep generative models are widely used for modelling high-dimensional time series, such as video animations, audio and climate data. Sequential variational autoencoders have been successfully considered for many applications, with many variant models relying on discrete-time methods and recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GPs), allowing inductive biases to be explicitly encoded via the kernel function and interpretability of the latent space. However, a major limitation of GPVAEs is that it inherits the same cubic computational cost as GPs. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable a linear-time GP solver via Kalman filtering and smoothing. We show via corrupt and missing frames tasks that our method performs favourably, especially on the latter where it outperforms RNN-based models.Comment: Non-archival paper presented at Workshop on Continuous Time Methods for Machine Learning. The 39th International Conference on Machine Learning, Baltimor

Joint object boundary and skeleton detection using convolutional neural networks

While the duality between boundary and medial representations has been exploited in the context of pre-segmented shapes, it has not been studied in the context of natural scenes. The goal of this project is to use a shared feature representation to address edge and skeleton detection simultaneously, improving performance for both tasks. To compare the relative benefits of a joint approach, we plan to use a single convolutional neural network (CNN) for both tasks, combined with a novel loss function that enforces consistency between detected boundary and medial points.Outgoin

Kausal upptäckt för villkorad stationär tidsseriedata : Mot kausal upptäckt i videor

Performing causal reasoning in a scene is an inherent mechanism in human cognition; however, the majority of approaches in the causality literature aiming for this task still consider constrained scenarios, such as simple physical systems or stationary time-series data. In this work we aim for causal discovery in videos concerning realistic scenarios. We gather motivation for causal discovery by acknowledging this task to be core at human cognition. Moreover, we interpret the scene as a composition of time-series that interact along the sequence and aim for modeling the non-stationary behaviors in a scene. We propose State-dependent Causal Inference (SDCI) for causal discovery in conditional stationary time-series data. We formulate our problem of causal analysis by considering that the stationarity of the time-series is conditioned on a categorical variable, which we call state. Results show that the probabilistic implementation proposed achieves outstanding results in identifying causal relations on simulated data. When considering the state being independent from the dynamics, our method maintains decent accuracy levels of edge-type identification achieving 74.87% test accuracy when considering a total of 8 states. Furthermore, our method correctly handles regimes where the state variable undergoes complex transitions and is dependent on the dynamics of the scene, achieving 79.21% accuracy in identifying the causal interactions. We consider this work to be an important contribution towards causal discovery in videos. Att utföra kausala resonemang i en scen är en medfödd mekanism i mänsklig kognition; dock betraktar fortfarande majoriteten av tillvägagångssätt i kausalitetslitteraturen, som syftar till denna uppgift, begränsade scenarier såsom enkla fysiska system eller stationära tidsseriedata. I detta arbete strävar vi efter kausal upptäckt i videor om realistiska scenarier. Vi samlar motivation för kausal upptäckt genom att erkänna att denna uppgift är kärnan i mänsklig kognition. Dessutom tolkar vi scenen som en komposition av tidsserier som interagerar längs sekvensen och syftar till att modellera det icke-stationära beteendet i en scen. Vi föreslår Tillståndsberoende kausal inferens (SDCI) för kausal upptäckt i villkorlig stationär tidsseriedata. Vi formulerar vårt problem med kausalanalys genom att anse att tidsseriens stationäritet är villkorad av en kategorisk variabel, som vi kallar tillstånd. Resultaten visar att det föreslagna probabilistiska genomförandet uppnår enastående resultat vid identifiering av orsakssambandet på simulerade data. När man överväger att tillståndet är oberoende av dynamiken, upprätthåller vår metod anständiga noggrannhetsnivåer av kanttypsidentifiering som uppnår 74, 87% testnoggrannhet när man överväger totalt 8 tillstånd. Dessutom hanterar vår metod korrekt regimer där tillståndsvariabeln genomgår komplexa övergångar och är beroende av dynamiken på scenen och uppnår 79, 21% noggrannhet för att identifiera kausala interaktioner. Vi anser att detta arbete är ett viktigt bidrag till kausal upptäckt i videor