Airship Formations for Animal Motion Capture and Behavior Analysis

Using UAVs for wildlife observation and motion capture offers manifold advantages for studying animals in the wild, especially grazing herds in open terrain. The aerial perspective allows observation at a scale and depth that is not possible on the ground, offering new insights into group behavior. However, the very nature of wildlife field-studies puts traditional fixed wing and multi-copter systems to their limits: limited flight time, noise and safety aspects affect their efficacy, where lighter than air systems can remain on station for many hours. Nevertheless, airships are challenging from a ground handling perspective as well as from a control point of view, being voluminous and highly affected by wind. In this work, we showcase a system designed to use airship formations to track, follow, and visually record wild horses from multiple angles, including airship design, simulation, control, on board computer vision, autonomous operation and practical aspects of field experiments.

Diffusion Posterior Sampling is Computationally Intractable

Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid y)$. Posterior sampling is useful for tasks such as inpainting, super-resolution, and MRI reconstruction, so a number of recent works have given algorithms to heuristically approximate it; but none are known to converge to the correct distribution in polynomial time. In this paper we show that posterior sampling is \emph{computationally intractable}: under the most basic assumption in cryptography -- that one-way functions exist -- there are instances for which \emph{every} algorithm takes superpolynomial time, even though \emph{unconditional} sampling is provably fast. We also show that the exponential-time rejection sampling algorithm is essentially optimal under the stronger plausible assumption that there are one-way functions that take exponential time to invert.

Sample-Efficient Training for Diffusion

Score-based diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. Recently, a number of theoretical works \citep{chen2022, Chen2022ImprovedAO, Chenetal23flowode, benton2023linear} have shown that diffusion models can efficiently sample, assuming $L^2$-accurate score estimates. The score-matching objective naturally approximates the true score in $L^2$, but the sample complexity of existing bounds depends \emph{polynomially} on the data radius and desired Wasserstein accuracy. By contrast, the time complexity of sampling is only logarithmic in these parameters. We show that estimating the score in $L^2$ \emph{requires} this polynomial dependence, but that a number of samples that scales polylogarithmically in the Wasserstein accuracy actually do suffice for sampling. We show that with a polylogarithmic number of samples, the ERM of the score-matching objective is $L^2$ accurate on all but a probability $\delta$ fraction of the true distribution, and that this weaker guarantee is sufficient for efficient sampling.

Sharp Noisy Binary Search with Monotonic Probabilities

We revisit the noisy binary search model of Karp and Kleinberg, in which we have $n$ coins with unknown probabilities $p_i$ that we can flip. The coins are sorted by increasing $p_i$, and we would like to find where the probability crosses (to within $\varepsilon$) of a target value $\tau$. This generalized the fixed-noise model of Burnashev and Zigangirov , in which $p_i = \frac{1}{2} \pm \varepsilon$, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that $\Theta(\frac{1}{\varepsilon^2} \log n)$ samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability $1-\delta$ from \[ \frac{1}{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} \frac{1}{\delta} + \log \frac{1}{\delta})\right) \] samples, where $C_{\tau, \varepsilon}$ is the optimal such constant achievable. For $\delta > n^{-o(1)}$ this is within $1 + o(1)$ of optimal, and for $\delta \ll 1$ it is the first bound within constant factors of optimal.

A Competitive Algorithm for Agnostic Active Learning

For some hypothesis classes and input distributions, active agnostic learning needs exponentially fewer samples than passive learning; for other classes and distributions, it offers little to no improvement. The most popular algorithms for agnostic active learning express their performance in terms of a parameter called the disagreement coefficient, but it is known that these algorithms are inefficient on some inputs. We take a different approach to agnostic active learning, getting an algorithm that is competitive with the optimal algorithm for any binary hypothesis class $H$ and distribution $D_X$ over $X$. In particular, if any algorithm can use $m^*$ queries to get $O(\eta)$ error, then our algorithm uses $O(m^* \log |H|)$ queries to get $O(\eta)$ error. Our algorithm lies in the vein of the splitting-based approach of Dasgupta [2004], which gets a similar result for the realizable ($\eta = 0$) setting. We also show that it is NP-hard to do better than our algorithm's $O(\log |H|)$ overhead in general.

Finite-Sample Symmetric Mean Estimation with Fisher Information Rate

The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved asymptotically to $\frac{1}{n\mathcal I}$, where $\mathcal I$ is the Fisher information of the distribution. Such an improvement is not possible for general unknown $f$, but [Stone, 1975] showed that this asymptotic convergence $\textit{is}$ possible if $f$ is $\textit{symmetric}$ about its mean. Stone's bound is asymptotic, however: the $n$ required for convergence depends in an unspecified way on the distribution $f$ and failure probability $\delta$. In this paper we give finite-sample guarantees for symmetric mean estimation in terms of Fisher information. For every $f, n, \delta$ with $n > \log \frac{1}{\delta}$, we get convergence close to a subgaussian with variance $\frac{1}{n \mathcal I_r}$, where $\mathcal I_r$ is the $r$-$\textit{smoothed}$ Fisher information with smoothing radius $r$ that decays polynomially in $n$. Such a bound essentially matches the finite-sample guarantees in the known-$f$ setting.

Accelerated Video Annotation driven by Deep Detector and Tracker

Annotating object ground truth in videos is vital for several downstream tasks in robot perception and machine learning, such as for evaluating the performance of an object tracker or training an image-based object detector. The accuracy of the annotated instances of the moving objects on every image frame in a video is crucially important. Achieving that through manual annotations is not only very time consuming and labor intensive, but is also prone to high error rate. State-of-the-art annotation methods depend on manually initializing the object bounding boxes only in the first frame and then use classical tracking methods, e.g., adaboost, or kernelized correlation filters, to keep track of those bounding boxes. These can quickly drift, thereby requiring tedious manual supervision. In this paper, we propose a new annotation method which leverages a combination of a learning-based detector (SSD) and a learning-based tracker (RE$^3$). Through this, we significantly reduce annotation drifts, and, consequently, the required manual supervision. We validate our approach through annotation experiments using our proposed annotation method and existing baselines on a set of drone video frames. Source code and detailed information on how to run the annotation program can be found at https://github.com/robot-perception-group/smarter-labelme

High-dimensional Location Estimation via Norm Concentration for Subgamma Vectors

In location estimation, we are given $n$ samples from a known distribution $f$ shifted by an unknown translation $\lambda$, and want to estimate $\lambda$ as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error $\mathcal N(0, \frac{1}{n\mathcal I})$, where $\mathcal I$ is the Fisher information of $f$. However, the $n$ required for convergence depends on $f$, and may be arbitrarily large. We build on the theory using \emph{smoothed} estimators to bound the error for finite $n$ in terms of $\mathcal I_r$, the Fisher information of the $r$-smoothed distribution. As $n \to \infty$, $r \to 0$ at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional $f$ to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Perception-driven Formation Control of Airships

For tracking and motion capture (MoCap) of animals in their natural habitat, a formation of safe and silent aerial platforms, such as airships with on-board cameras, is well suited. However, unlike multi-rotors, airships are severely motion constrained and affected by ambient wind. Their orientation and flight direction are also tightly coupled. Therefore, state-of-the-art MPC-based formation control methods for perception tasks are not directly applicable for a team of airships. In this paper, we address this problem by first exploiting a periodic relationship between the airspeed of an airship and its distance to the subject. We use it to derive analytical and numeric solutions that satisfy the MoCap perception constraints. Based on this, we develop an MPC-based formation controller. We performed detailed analysis of our solution, including the effects of changing physical parameters (like angle of attack and pitch angle) on it. Extensive simulation experiments, comparing results for different formation sizes, different wind conditions and various subject speeds, are presented. A demonstration of our method on a real airship is also included. We have released all of our source code at https://github.com/robot-perception-group/Airship-MPC. A video describing our approach and results can be watched at https://youtu.be/ihS0_VRD_kk

Hardness and Algorithms for Robust and Sparse Optimization

We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the goal of the robust linear regression problem is to identify a small number of erroneous measurements. Specifically, the sparse linear regression problem seeks a $k$-sparse vector $x\in\mathbb{R}^d$ to minimize $\|Ax-b\|_2$, given an input matrix $A\in\mathbb{R}^{n\times d}$ and a target vector $b\in\mathbb{R}^n$, while the robust linear regression problem seeks a set $S$ that ignores at most $k$ rows and a vector $x$ to minimize $\|(Ax-b)_S\|_2$. We first show bicriteria, NP-hardness of approximation for robust regression building on the work of [OWZ15] which implies a similar result for sparse regression. We further show fine-grained hardness of robust regression through a reduction from the minimum-weight $k$-clique conjecture. On the positive side, we give an algorithm for robust regression that achieves arbitrarily accurate additive error and uses runtime that closely matches the lower bound from the fine-grained hardness result, as well as an algorithm for sparse regression with similar runtime. Both our upper and lower bounds rely on a general reduction from robust linear regression to sparse regression that we introduce. Our algorithms, inspired by the 3SUM problem, use approximate nearest neighbor data structures and may be of independent interest for solving sparse optimization problems. For instance, we demonstrate that our techniques can also be used for the well-studied sparse PCA problem.