Daily Papers

The Kalman filter has been adopted in acoustic echo cancellation due to its robustness to double-talk, fast convergence, and good steady-state performance. The performance of Kalman filter is closely related to the estimation accuracy of the state noise covariance and the observation noise covariance. The estimation error may lead to unacceptable results, especially when the echo path suffers abrupt changes, the tracking performance of the Kalman filter could be degraded significantly. In this paper, we propose the neural Kalman filtering (NKF), which uses neural networks to implicitly model the covariance of the state noise and observation noise and to output the Kalman gain in real-time. Experimental results on both synthetic test sets and real-recorded test sets show that, the proposed NKF has superior convergence and re-convergence performance while ensuring low near-end speech degradation comparing with the state-of-the-art model-based methods. Moreover, the model size of the proposed NKF is merely 5.3 K and the RTF is as low as 0.09, which indicates that it can be deployed in low-resource platforms.

Despite the promising progress of face image super-resolution, video face super-resolution remains relatively under-explored. Existing approaches either adapt general video super-resolution networks to face datasets or apply established face image super-resolution models independently on individual video frames. These paradigms encounter challenges either in reconstructing facial details or maintaining temporal consistency. To address these issues, we introduce a novel framework called Kalman-inspired Feature Propagation (KEEP), designed to maintain a stable face prior over time. The Kalman filtering principles offer our method a recurrent ability to use the information from previously restored frames to guide and regulate the restoration process of the current frame. Extensive experiments demonstrate the effectiveness of our method in capturing facial details consistently across video frames. Code and video demo are available at https://jnjaby.github.io/projects/KEEP.

Reinforcement learning (RL) tackles sequential decision-making problems by creating agents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model parameters to maximize expected rewards, neglecting the stochastic dynamics of agent-environment interactions and the critical role of uncertainty quantification. Our research leverages the Kalman filtering paradigm to introduce a novel and scalable sampling algorithm called Langevinized Kalman Temporal-Difference (LKTD) for deep reinforcement learning. This algorithm, grounded in Stochastic Gradient Markov Chain Monte Carlo (SGMCMC), efficiently draws samples from the posterior distribution of deep neural network parameters. Under mild conditions, we prove that the posterior samples generated by the LKTD algorithm converge to a stationary distribution. This convergence not only enables us to quantify uncertainties associated with the value function and model parameters but also allows us to monitor these uncertainties during policy updates throughout the training phase. The LKTD algorithm paves the way for more robust and adaptable reinforcement learning approaches.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as 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 (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.

Many Multi-Object Tracking (MOT) approaches exploit motion information to associate all the detected objects across frames. However, many methods that rely on filtering-based algorithms, such as the Kalman Filter, often work well in linear motion scenarios but struggle to accurately predict the locations of objects undergoing complex and non-linear movements. To tackle these scenarios, we propose a motion-based MOT approach with an enhanced temporal motion predictor, ETTrack. Specifically, the motion predictor integrates a transformer model and a Temporal Convolutional Network (TCN) to capture short-term and long-term motion patterns, and it predicts the future motion of individual objects based on the historical motion information. Additionally, we propose a novel Momentum Correction Loss function that provides additional information regarding the motion direction of objects during training. This allows the motion predictor rapidly adapt to motion variations and more accurately predict future motion. Our experimental results demonstrate that ETTrack achieves a competitive performance compared with state-of-the-art trackers on DanceTrack and SportsMOT, scoring 56.4% and 74.4% in HOTA metrics, respectively.

The Variational Autoencoder (VAE) is a seminal approach in deep generative modeling with latent variables. Interpreting its reconstruction process as a nonlinear transformation of samples from the latent posterior distribution, we apply the Unscented Transform (UT) -- a well-known distribution approximation used in the Unscented Kalman Filter (UKF) from the field of filtering. A finite set of statistics called sigma points, sampled deterministically, provides a more informative and lower-variance posterior representation than the ubiquitous noise-scaling of the reparameterization trick, while ensuring higher-quality reconstruction. We further boost the performance by replacing the Kullback-Leibler (KL) divergence with the Wasserstein distribution metric that allows for a sharper posterior. Inspired by the two components, we derive a novel, deterministic-sampling flavor of the VAE, the Unscented Autoencoder (UAE), trained purely with regularization-like terms on the per-sample posterior. We empirically show competitive performance in Fr\'echet Inception Distance (FID) scores over closely-related models, in addition to a lower training variance than the VAE.