In this note, we revisit non-stationary linear bandits, a variant of stochastic linear bandits with a time-varying underlying regression parameter. Existing studies develop various algorithms and show that they enjoy an $\widetilde{O}(T^{2/3}(1+P_T)^{1/3})$ dynamic regret, where $T$ is the time horizon and $P_T$ is the path-length that measures the fluctuation of the evolving unknown parameter. However, we discover that a serious technical flaw makes the argument ungrounded. We revisit the analysis and present a fix. Without modifying original algorithms, we can prove an $\widetilde{O}(T^{3/4}(1+P_T)^{1/4})$ dynamic regret for these algorithms, slightly worse than the rate as was anticipated. We also show some impossibility results for the key quantity concerned in the regret analysis. Note that the above dynamic regret guarantee requires an oracle knowledge of the path-length $P_T$. Combining the bandit-over-bandit mechanism, we can also achieve the same guarantee in a parameter-free way.
Normalizing flows are a widely used class of latent-variable generative models with a tractable likelihood. Affine-coupling (Dinh et al, 2014-16) models are a particularly common type of normalizing flows, for which the Jacobian of the latent-to-observable-variable transformation is triangular, allowing the likelihood to be computed in linear time. Despite the widespread usage of affine couplings, the special structure of the architecture makes understanding their representational power challenging. The question of universal approximation was only recently resolved by three parallel papers (Huang et al.,2020;Zhang et al.,2020;Koehler et al.,2020) -- who showed reasonably regular distributions can be approximated arbitrarily well using affine couplings -- albeit with networks with a nearly-singular Jacobian. As ill-conditioned Jacobians are an obstacle for likelihood-based training, the fundamental question remains: which distributions can be approximated using well-conditioned affine coupling flows? In this paper, we show that any log-concave distribution can be approximated using well-conditioned affine-coupling flows. In terms of proof techniques, we uncover and leverage deep connections between affine coupling architectures, underdamped Langevin dynamics (a stochastic differential equation often used to sample from Gibbs measures) and H\'enon maps (a structured dynamical system that appears in the study of symplectic diffeomorphisms). Our results also inform the practice of training affine couplings: we approximate a padded version of the input distribution with iid Gaussians -- a strategy which Koehler et al.(2020) empirically observed to result in better-conditioned flows, but had hitherto no theoretical grounding. Our proof can thus be seen as providing theoretical evidence for the benefits of Gaussian padding when training normalizing flows.
Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over entropy functionals in Wasserstein space. This equivalence, introduced by Jordan, Kinderlehrer and Otto, inspired the so-called JKO scheme to approximate these diffusion processes via an implicit discretization of the gradient flow in Wasserstein space. Solving the optimization problem associated to each JKO step, however, presents serious computational challenges. We introduce a scalable method to approximate Wasserstein gradient flows, targeted to machine learning applications. Our approach relies on input-convex neural networks (ICNNs) to discretize the JKO steps, which can be optimized by stochastic gradient descent. Unlike previous work, our method does not require domain discretization or particle simulation. As a result, we can sample from the measure at each time step of the diffusion and compute its probability density. We demonstrate our algorithm's performance by computing diffusions following the Fokker-Planck equation and apply it to unnormalized density sampling as well as nonlinear filtering.
In this work, we present a Quantum Hopfield Associative Memory (QHAM) and demonstrate its capabilities in simulation and hardware using IBM Quantum Experience. The QHAM is based on a quantum neuron design which can be utilized for many different machine learning applications and can be implemented on real quantum hardware without requiring mid-circuit measurement or reset operations. We analyze the accuracy of the neuron and the full QHAM considering hardware errors via simulation with hardware noise models as well as with implementation on the 15-qubit ibmq_16_melbourne device. The quantum neuron and the QHAM are shown to be resilient to noise and require low qubit and time overhead. We benchmark the QHAM by testing its effective memory capacity against qubit- and circuit-level errors and demonstrate its capabilities in the NISQ-era of quantum hardware. This demonstration of the first functional QHAM to be implemented in NISQ-era quantum hardware is a significant step in machine learning at the leading edge of quantum computing.
Cognitive radio (CR) is a promising technology enabling efficient utilization of the spectrum resource for future wireless systems. As future CR networks are envisioned to operate over a wide frequency range, advanced wideband spectrum sensing (WBSS) capable of quickly and reliably detecting idle spectrum bands across a wide frequency span is essential. In this article, we provide an overview of recent advances on sub-Nyquist sampling-based WBSS techniques, including compressed sensing-based methods and compressive covariance sensing-based methods. An elaborate discussion of the pros and cons of each approach is presented, along with some challenging issues for future research. A comparative study suggests that the compressive covariance sensing-based approach offers a more competitive solution for reliable real-time WBSS.
Reconfigurable intelligent surface (RIS)-empowered communications is on the rise and is a promising technology envisioned to aid in 6G and beyond wireless communication networks. RISs can manipulate impinging waves through their electromagnetic elements enabling some sort of a control over the wireless channel. In this paper, the potential of RIS technology is explored to perform equalization over-the-air for frequency-selective channels whereas, equalization is generally conducted at either the transmitter or receiver in conventional communication systems. Specifically, with the aid of an RIS, the frequency-selective channel from the transmitter to the RIS is transformed to a frequency-flat channel through elimination of inter-symbol interference (ISI) components at the receiver. ISI is eliminated by adjusting the phases of impinging signals particularly to maximize the incoming signal of the strongest tap. First, a general end-to-end system model is provided and a continuous to discrete-time signal model is presented. Subsequently, a probabilistic analysis for the elimination of ISI terms is conducted and reinforced with computer simulations. Furthermore, a theoretical error probability analysis is performed along with computer simulations. It is demonstrated that with the proposed method, ISI can successfully be eliminated and the RIS-aided communication channel can be converted from frequency-selective to frequency-flat.
Maximising a cumulative reward function that is Markov and stationary, i.e., defined over state-action pairs and independent of time, is sufficient to capture many kinds of goals in a Markov Decision Process (MDP) based on the Reinforcement Learning (RL) problem formulation. However, not all goals can be captured in this manner. Specifically, it is easy to see that Convex MDPs in which goals are expressed as convex functions of stationary distributions cannot, in general, be formulated in this manner. In this paper, we reformulate the convex MDP problem as a min-max game between the policy and cost (negative reward) players using Fenchel duality and propose a meta-algorithm for solving it. We show that the average of the policies produced by an RL agent that maximizes the non-stationary reward produced by the cost player converges to an optimal solution to the convex MDP. Finally, we show that the meta-algorithm unifies several disparate branches of reinforcement learning algorithms in the literature, such as apprenticeship learning, variational intrinsic control, constrained MDPs, and pure exploration into a single framework.
The research direction of identifying acoustic bio-markers of respiratory diseases has received renewed interest following the onset of COVID-19 pandemic. In this paper, we design an approach to COVID-19 diagnostic using crowd-sourced multi-modal data. The data resource, consisting of acoustic signals like cough, breathing, and speech signals, along with the data of symptoms, are recorded using a web-application over a period of ten months. We investigate the use of statistical descriptors of simple time-frequency features for acoustic signals and binary features for the presence of symptoms. Unlike previous works, we primarily focus on the application of simple linear classifiers like logistic regression and support vector machines for acoustic data while decision tree models are employed on the symptoms data. We show that a multi-modal integration of acoustics and symptoms classifiers achieves an area-under-curve (AUC) of 92.40, a significant improvement over any individual modality. Several ablation experiments are also provided which highlight the acoustic and symptom dimensions that are important for the task of COVID-19 diagnostics.
In this paper we propose a data augmentation method for time series with irregular sampling, Time-Conditional Generative Adversarial Network (T-CGAN). Our approach is based on Conditional Generative Adversarial Networks (CGAN), where the generative step is implemented by a deconvolutional NN and the discriminative step by a convolutional NN. Both the generator and the discriminator are conditioned on the sampling timestamps, to learn the hidden relationship between data and timestamps, and consequently to generate new time series. We evaluate our model with synthetic and real-world datasets. For the synthetic data, we compare the performance of a classifier trained with T-CGAN-generated data, against the performance of the same classifier trained on the original data. Results show that classifiers trained on T-CGAN-generated data perform the same as classifiers trained on real data, even with very short time series and small training sets. For the real world datasets, we compare our method with other techniques of data augmentation for time series, such as time slicing and time warping, over a classification problem with unbalanced datasets. Results show that our method always outperforms the other approaches, both in case of regularly sampled and irregularly sampled time series. We achieve particularly good performance in case with a small training set and short, noisy, irregularly-sampled time series.
We propose a novel weakly supervised method to improve the boundary of the 3D segmented nuclei utilizing an over-segmented image. This is motivated by the observation that current state-of-the-art deep learning methods do not result in accurate boundaries when the training data is weakly annotated. Towards this, a 3D U-Net is trained to get the centroid of the nuclei and integrated with a simple linear iterative clustering (SLIC) supervoxel algorithm that provides better adherence to cluster boundaries. To track these segmented nuclei, our algorithm utilizes the relative nuclei location depicting the processes of nuclei division and apoptosis. The proposed algorithmic pipeline achieves better segmentation performance compared to the state-of-the-art method in Cell Tracking Challenge (CTC) 2019 and comparable performance to state-of-the-art methods in IEEE ISBI CTC2020 while utilizing very few pixel-wise annotated data. Detailed experimental results are provided, and the source code is available on GitHub.