Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the tempered Bayes filter, improving estimation performance through both of the aforementioned, and one newly introduced, modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that -- besides the well-known fact in the field of Bayesian inference that likelihood tempering affects the balance between prior and likelihood -- full-posterior tempering tunes the level of entropy in the final belief distribution. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter achieves improved predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance propagation. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.

Navigating efficiently to an object in an unexplored environment is a critical skill for general-purpose intelligent robots. Recent approaches to this object goal navigation problem have embraced a modular strategy, integrating classical exploration algorithms-notably frontier exploration-with a learned semantic mapping/exploration module. This paper introduces a novel informative path planning and 3D object probability mapping approach. The mapping module computes the probability of the object of interest through semantic segmentation and a Bayes filter. Additionally, it stores probabilities for common objects, which semantically guides the exploration based on common sense priors from a large language model. The planner terminates when the current viewpoint captures enough voxels identified with high confidence as the object of interest. Although our planner follows a zero-shot approach, it achieves state-of-the-art performance as measured by the Success weighted by Path Length (SPL) and Soft SPL in the Habitat ObjectNav Challenge 2023, outperforming other works by more than 20%. Furthermore, we validate its effectiveness on real robots. Project webpage: https://ippon-paper.github.io/

We study pursuit-evasion games in highly occluded urban environments, e.g. tall buildings in a city, where a scout (quadrotor) tracks multiple dynamic targets on the ground. We show that we can build a neural radiance field (NeRF) representation of the city -- online -- using RGB and depth images from different vantage points. This representation is used to calculate the information gain to both explore unknown parts of the city and track the targets -- thereby giving a completely first-principles approach to actively tracking dynamic targets. We demonstrate, using a custom-built simulator using Open Street Maps data of Philadelphia and New York City, that we can explore and locate 20 stationary targets within 300 steps. This is slower than a greedy baseline which which does not use active perception. But for dynamic targets that actively hide behind occlusions, we show that our approach maintains, at worst, a tracking error of 200m; the greedy baseline can have a tracking error as large as 600m. We observe a number of interesting properties in the scout's policies, e.g., it switches its attention to track a different target periodically, as the quality of the NeRF representation improves over time, the scout also becomes better in terms of target tracking.

This paper presents a formal verification guided approach for a principled design and implementation of robust and resilient learning-enabled systems. We focus on learning-enabled state estimation systems (LE-SESs), which have been widely used in robotics applications to determine the current state (e.g., location, speed, direction, etc.) of a complex system. The LE-SESs are networked systems composed of a set of connected components including Bayes filters for localisation, and neural networks for processing sensory input. We study LE-SESs from the perspective of formal verification, which determines the satisfiability of a system model against the specified properties. Over LE-SESs, we investigate two key properties - robustness and resilience - and provide their formal definitions. To enable formal verification, we reduce the LE-SESs to a novel class of labelled transition systems, named {PO}2-LTS in the paper, and formally express the properties as constrained optimisation objectives. We prove that the robustness verification is NP-complete. Based on {PO}2-LTS and the optimisation objectives, practical verification algorithms are developed to check the satisfiability of the properties on the LE-SESs. As a major case study, we interrogate a real-world dynamic tracking system which uses a single Kalman Filter (KF) - a special case of Bayes filter - to localise and track a ground vehicle. Its perception system, based on convolutional neural networks, processes a high-resolution Wide Area Motion Imagery (WAMI) data stream. Experimental results show that our algorithms can not only verify the properties of the WAMI tracking system but also provide representative examples, the latter of which inspired us to take an enhanced LE-SESs design where runtime monitors or joint-KFs are required. Experimental results confirm the improvement of the robustness of the enhanced design.

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the distribution with a weighted sum of functions from a set of continuous functions. Central to the approach is the use of sampling to approximate multiplications in the Bayes filter. We provide theoretical analysis, giving conditions for sampling to give good approximation. We next specialize to the case of weighted sums of Gaussians, and show how properties of Gaussians enable closed-form transition and efficient multiplication. Lastly, we conduct preliminary experiments on a robot localization problem and compare performance with the particle filter, to demonstrate the potential of the proposed method.

As a new sub-discipline of Data Science, I notice that SYSTEMS Analytics is starting to get some traction! There are a couple of Analytics graduate level programs with *Systems* in its title (Stevens Institute of Technology and University of North Carolina are the only ones I know). Web search brings up NO books on *Systems* Analytics. With the publication of my book with *Systems* in the title, that gap has been filled now! "SYSTEMS Analytics: Adaptive Machine Learning workbook". My last Analytics startup launched in 2013 explicitly used SYSTEMS Analytics in our Retail Recommendation and Uplift SaaS product; my initial bias for the Systems approach was confirmed by the success of our product.

When you Google "Kalman Filter AND Machine Learning", very few interesting references pop up! Perhaps my search terms are not the best, perhaps Fintech guys keep such algorithms close to their vests, perhaps there is not much of work done in bringing these two incredibly powerful tools together... In any case, Part II of my new book, "Systems Analytics: Adaptive Machine Learning workbook" focuses exactly on this merger. I am happy to report that pre-publication copy of my book (including MATLAB code) is available for download for FREE. See the end of this blog for how . . .

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli which caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. In this paper we present a method for learning to approximate a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of probabilistic population codes to compute Bayes' rule, and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem, and show how the hidden layer of the neural network develops tuning curves which are consistent with findings in experimental neuroscience.

As a new sub-discipline of Data Science, I notice that SYSTEMS Analytics is starting to get some traction! There are a couple of Analytics graduate level programs with *Systems* in its title (Stevens Institute of Technology and University of North Carolina are the only ones I know). Web search brings up NO books on *Systems* Analytics. With the publication of my book with *Systems* in the title, that gap has been filled now! "SYSTEMS Analytics: Adaptive Machine Learning workbook". My last Analytics startup launched in 2013 explicitly used SYSTEMS Analytics in our Retail Recommendation and Uplift SaaS product; my initial bias for the Systems approach was confirmed by the success of our product.

As a new sub-discipline of Data Science, I notice that SYSTEMS Analytics is starting to get some traction! There are a couple of Analytics graduate level programs with *Systems* in its title (Stevens Institute of Technology and University of North Carolina are the only ones I know). Web search brings up NO books on *Systems* Analytics. With the publication of my book with *Systems* in the title, that gap has been filled now! "SYSTEMS Analytics: Adaptive Machine Learning workbook". My last Analytics startup launched in 2013 explicitly used SYSTEMS Analytics in our Retail Recommendation and Uplift SaaS product; my initial bias for the Systems approach was confirmed by the success of our product.