We propose a new penalty, named as the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback penalty is a weakly convex function, and it bears various theoretical and computational advantages of both the benchmark convex $\ell_1$ penalty and many of its non-convex surrogates that have been well studied in the literature. For the recovery model using the springback penalty, we establish the exact and stable recovery theory for both sparse and nearly sparse signals, respectively, and derive an easily implementable difference-of-convex algorithm. In particular, we show its theoretical superiority to some existing models with a sharper recovery bound for some scenarios where the level of measurement noise is large or the amount of measurements is limited, and demonstrate its numerical robustness regardless of varying coherence of the sensing matrix. Because of its theoretical guarantee of recovery with severe measurements, computational tractability, and numerical robustness for ill-conditioned sensing matrices, the springback penalty is particularly favorable for the scenario where the incomplete and inaccurate measurements are collected by coherence-hidden or -static sensing hardware.
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In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample covariance matrix of some given training data, but, as is well-known, the performance of such filters is poor when the number of training data $n$ is not much larger than the data dimension $p$. We thus seek a covariance estimator to replace sample covariance. To account for the fact that $n$ and $p$ may be of comparable size, we adopt the "large-dimensional asymptotic model" in which $n$ and $p$ go to infinity in a fixed ratio. Under this assumption, we identify a covariance estimator that is asymptotically detection-theoretic optimal within a general shrinkage class inspired by C. Stein, and we give consistent estimates for conditional false-alarm and detection rate of the corresponding adaptive matched filter.
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the objective is given as an expectation of a function given as a solution to a random optimization problem. We employ the structure of the problem and obtain a convex-concave stochastic saddle-point reformulation of this problem. In the setting when the distribution of random probability measures is discrete, we propose a stochastic optimization algorithm and estimate its complexity. The second result, based on kernel methods, extends the previous one to the arbitrary distribution of random probability measures. Moreover, this new algorithm has a total complexity better than the Stochastic Approximation approach combined with the Sinkhorn algorithm in many cases. We also illustrate our developments by a series of numerical experiments.
Recently, RobustBench (Croce et al. 2020) has become a widely recognized benchmark for the adversarial robustness of image classification networks. In its most commonly reported sub-task, RobustBench evaluates and ranks the adversarial robustness of trained neural networks on CIFAR10 under AutoAttack (Croce and Hein 2020b) with l-inf perturbations limited to eps = 8/255. With leading scores of the currently best performing models of around 60% of the baseline, it is fair to characterize this benchmark to be quite challenging. Despite its general acceptance in recent literature, we aim to foster discussion about the suitability of RobustBench as a key indicator for robustness which could be generalized to practical applications. Our line of argumentation against this is two-fold and supported by excessive experiments presented in this paper: We argue that I) the alternation of data by AutoAttack with l-inf, eps = 8/255 is unrealistically strong, resulting in close to perfect detection rates of adversarial samples even by simple detection algorithms and human observers. We also show that other attack methods are much harder to detect while achieving similar success rates. II) That results on low-resolution data sets like CIFAR10 do not generalize well to higher resolution images as gradient-based attacks appear to become even more detectable with increasing resolutions.
Recent studies have shown the vulnerability of reinforcement learning (RL) models in noisy settings. The sources of noises differ across scenarios. For instance, in practice, the observed reward channel is often subject to noise (e.g., when observed rewards are collected through sensors), and thus observed rewards may not be credible as a result. Also, in applications such as robotics, a deep reinforcement learning (DRL) algorithm can be manipulated to produce arbitrary errors. In this paper, we consider noisy RL problems where observed rewards by RL agents are generated with a reward confusion matrix. We call such observed rewards as perturbed rewards. We develop an unbiased reward estimator aided robust RL framework that enables RL agents to learn in noisy environments while observing only perturbed rewards. Our framework draws upon approaches for supervised learning with noisy data. The core ideas of our solution include estimating a reward confusion matrix and defining a set of unbiased surrogate rewards. We prove the convergence and sample complexity of our approach. Extensive experiments on different DRL platforms show that policies based on our estimated surrogate reward can achieve higher expected rewards, and converge faster than existing baselines. For instance, the state-of-the-art PPO algorithm is able to obtain 67.5% and 46.7% improvements in average on five Atari games, when the error rates are 10% and 30% respectively.
This study evaluates the performances of CNN and LSTM for recognizing common charts patterns in a stock historical data. It presents two common patterns, the method used to build the training set, the neural networks architectures and the accuracies obtained.
Incremental improvements in accuracy of Convolutional Neural Networks are usually achieved through use of deeper and more complex models trained on larger datasets. However, enlarging dataset and models increases the computation and storage costs and cannot be done indefinitely. In this work, we seek to improve the identification and verification accuracy of a text-independent speaker recognition system without use of extra data or deeper and more complex models by augmenting the training and testing data, finding the optimal dimensionality of embedding space and use of more discriminative loss functions. Results of experiments on VoxCeleb dataset suggest that: (i) Simple repetition and random time-reversion of utterances can reduce prediction errors by up to 18%. (ii) Lower dimensional embeddings are more suitable for verification. (iii) Use of proposed logistic margin loss function leads to unified embeddings with state-of-the-art identification and competitive verification accuracies.
Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.
We study the problem of named entity recognition (NER) from electronic medical records, which is one of the most fundamental and critical problems for medical text mining. Medical records which are written by clinicians from different specialties usually contain quite different terminologies and writing styles. The difference of specialties and the cost of human annotation makes it particularly difficult to train a universal medical NER system. In this paper, we propose a label-aware double transfer learning framework (La-DTL) for cross-specialty NER, so that a medical NER system designed for one specialty could be conveniently applied to another one with minimal annotation efforts. The transferability is guaranteed by two components: (i) we propose label-aware MMD for feature representation transfer, and (ii) we perform parameter transfer with a theoretical upper bound which is also label aware. We conduct extensive experiments on 12 cross-specialty NER tasks. The experimental results demonstrate that La-DTL provides consistent accuracy improvement over strong baselines. Besides, the promising experimental results on non-medical NER scenarios indicate that La-DTL is potential to be seamlessly adapted to a wide range of NER tasks.
This paper proposes a method for generating speech from filterbank mel frequency cepstral coefficients (MFCC), which are widely used in speech applications, such as ASR, but are generally considered unusable for speech synthesis. First, we predict fundamental frequency and voicing information from MFCCs with an autoregressive recurrent neural net. Second, the spectral envelope information contained in MFCCs is converted to all-pole filters, and a pitch-synchronous excitation model matched to these filters is trained. Finally, we introduce a generative adversarial network -based noise model to add a realistic high-frequency stochastic component to the modeled excitation signal. The results show that high quality speech reconstruction can be obtained, given only MFCC information at test time.
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer science has shown that, in appropriate distributional models, it is possible to robustly estimate the mean and covariance with polynomial time algorithms that can tolerate a constant fraction of corruptions, independent of the dimension. However, the sample and time complexity of these algorithms is prohibitively large for high-dimensional applications. In this work, we address both of these issues by establishing sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions. Finally, we show on both synthetic and real data that our algorithms have state-of-the-art performance and suddenly make high-dimensional robust estimation a realistic possibility.
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