A Forster transform is an operation that turns a distribution into one with good anti-concentration properties. While a Forster transform does not always exist, we show that any distribution can be efficiently decomposed as a disjoint mixture of few distributions for which a Forster transform exists and can be computed efficiently. As the main application of this result, we obtain the first polynomial-time algorithm for distribution-independent PAC learning of halfspaces in the Massart noise model with strongly polynomial sample complexity, i.e., independent of the bit complexity of the examples. Previous algorithms for this learning problem incurred sample complexity scaling polynomially with the bit complexity, even though such a dependence is not information-theoretically necessary.
In this work, we explore the problem of aligning two time-ordered point clouds which are spatially transformed and re-parameterized versions of each other. This has a diverse array of applications such as cross modal time series synchronization (e.g. MOCAP to video) and alignment of discretized curves in images. Most other works that address this problem attempt to jointly uncover a spatial alignment and correspondences between the two point clouds, or to derive local invariants to spatial transformations such as curvature before computing correspondences. By contrast, we sidestep spatial alignment completely by using self-similarity matrices (SSMs) as a proxy to the time-ordered point clouds, since self-similarity matrices are blind to isometries and respect global geometry. Our algorithm, dubbed "Isometry Blind Dynamic Time Warping" (IBDTW), is simple and general, and we show that its associated dissimilarity measure lower bounds the L1 Gromov-Hausdorff distance between the two point sets when restricted to warping paths. We also present a local, partial alignment extension of IBDTW based on the Smith Waterman algorithm. This eliminates the need for tedious manual cropping of time series, which is ordinarily necessary for global alignment algorithms to function properly.
Although modern object detection and classification models achieve high accuracy, these are typically constrained in advance on a fixed train set and are therefore not flexible to deal with novel, unseen object categories. Moreover, these models most often operate on a single frame, which may yield incorrect classifications in case of ambiguous viewpoints. In this paper, we propose an active inference agent that actively gathers evidence for object classifications, and can learn novel object categories over time. Drawing inspiration from the human brain, we build object-centric generative models composed of two information streams, a what- and a where-stream. The what-stream predicts whether the observed object belongs to a specific category, while the where-stream is responsible for representing the object in its internal 3D reference frame. We show that our agent (i) is able to learn representations for many object categories in an unsupervised way, (ii) achieves state-of-the-art classification accuracies, actively resolving ambiguity when required and (iii) identifies novel object categories. Furthermore, we validate our system in an end-to-end fashion where the agent is able to search for an object at a given pose from a pixel-based rendering. We believe that this is a first step towards building modular, intelligent systems that can be used for a wide range of tasks involving three dimensional objects.
Knowing the geometrical and acoustical parameters of a room may benefit applications such as audio augmented reality, speech dereverberation or audio forensics. In this paper, we study the problem of jointly estimating the total surface area, the volume, as well as the frequency-dependent reverberation time and mean surface absorption of a room in a blind fashion, based on two-channel noisy speech recordings from multiple, unknown source-receiver positions. A novel convolutional neural network architecture leveraging both single- and inter-channel cues is proposed and trained on a large, realistic simulated dataset. Results on both simulated and real data show that using multiple observations in one room significantly reduces estimation errors and variances on all target quantities, and that using two channels helps the estimation of surface and volume. The proposed model outperforms a recently proposed blind volume estimation method on the considered datasets.
The standard chirplet transform (CT) with a chirp-modulated Gaussian window provides a valuable tool for analyzing linear chirp signals. The parameters present in the window determine the performance of CT and play a very important role in high-resolution time-frequency (TF) analysis. In this paper, we first give the window shape analysis of CT and compare it with the extension that employs a rotating Gaussian window by fractional Fourier transform. The given parameters analysis provides certain theoretical guidance for developing high-resolution CT. We then propose a multi-resolution chirplet transform (MrCT) by combining multiple CTs with different parameter combinations. These are combined geometrically to obtain an improved TF resolution by overcoming the limitations of any single representation of the CT. By deriving the combined instantaneous frequency equation, we further develop a high-concentration TF post-processing approach to improve the readability of the MrCT. Numerical experiments on simulated and real signals verify its effectiveness.
Times series classification can be successfully tackled by jointly learning a shapelet-based representation of the series in the dataset and classifying the series according to this representation. However, although the learned shapelets are discriminative, they are not always similar to pieces of a real series in the dataset. This makes it difficult to interpret the decision, i.e. difficult to analyze if there are particular behaviors in a series that triggered the decision. In this paper, we make use of a simple convolutional network to tackle the time series classification task and we introduce an adversarial regularization to constrain the model to learn more interpretable shapelets. Our classification results on all the usual time series benchmarks are comparable with the results obtained by similar state-of-the-art algorithms but our adversarially regularized method learns shapelets that are, by design, interpretable.
In self driving car applications, there is a requirement to predict the location of the lane given an input RGB front facing image. In this paper, we propose an architecture that allows us to increase the speed and robustness of road detection without a large hit in accuracy by introducing an underlying shared feature space that is propagated over time, which serves as a flowing dynamic memory. By utilizing the gist of previous frames, we train the network to predict the current road with a greater accuracy and lesser deviation from previous frames.
Circadian and other physiological rhythms play a key role in both normal homeostasis and disease processes. Such is the case of circadian and infradian seizure patterns observed in epilepsy. However, these rhythms are not fully exploited in the design of active implantable medical devices. In this paper we explore a new implantable stimulator that implements chronotherapy as a feedforward input to supplement both open-loop and closed-loop methods. This integrated algorithm allows for stimulation to be adjusted to the ultradian, circadian, and infradian patterns observed in patients through slowly-varying temporal adjustments of stimulation and algorithm sub-components, while also enabling adaption of stimulation based on immediate physiological needs such as a breakthrough seizure or change of posture. Embedded physiological sensors in the stimulator can be used to refine the baseline stimulation circadian pattern as a "digital zeitgeber". This algorithmic approach is tested on a canine with severe drug-resistant idiopathic generalized epilepsy exhibiting a characteristic diurnal pattern correlated with sleep-wake cycles. Prior to implantation, the canine's cluster seizures evolved to status epilepticus (SE) and required emergency pharmacological intervention. The cranially-mounted system was fully-implanted bilaterally into the centromedian nucleus of the thalamus. Using combinations of time-based modulation, thalamocortical rhythm-specific tuning of frequency parameters, and fast-adaptive modes based on activity, the canine has experienced no further SE events post-implant at the time of writing (7 months), and no significant clusters are observed any longer. The use of digitally-enabled chronotherapy as a feedforward signal to augment adaptive neurostimulators could prove a useful algorithmic method where sensitivity to temporal patterns are characteristics of the disease state.
Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of the state-space, deal only with a convex fragment of temporal logic, or are not provably complete. We propose a scalable, provably complete algorithm that synthesizes continuous trajectories to satisfy non-convex \gls*{rtl} specifications. We separate discrete task planning and continuous motion planning on-the-fly and harness highly efficient boolean satisfiability (SAT) and \gls*{lp} solvers to find dynamically feasible trajectories that satisfy non-convex \gls*{rtl} specifications for high dimensional systems. The proposed design algorithms are proven sound and complete, and simulation results demonstrate our approach's scalability.
In this work, we present a comparative analysis of the trajectories estimated from various Simultaneous Localization and Mapping (SLAM) systems in a simulation environment for vineyards. Vineyard environment is challenging for SLAM methods, due to visual appearance changes over time, uneven terrain, and repeated visual patterns. For this reason, we created a simulation environment specifically for vineyards to help studying SLAM systems in such a challenging environment. We evaluated the following SLAM systems: LIO-SAM, StaticMapping, ORB-SLAM2, and RTAB-MAP in four different scenarios. The mobile robot used in this study equipped with 2D and 3D lidars, IMU, and RGB-D camera (Kinect v2). The results show good and encouraging performance of RTAB-MAP in such an environment.