Recent research shows that the following two models are equivalent: (a) infinitely wide neural networks (NNs) trained under l2 loss by gradient descent with infinitesimally small learning rate (b) kernel regression with respect to so-called Neural Tangent Kernels (NTKs) (Jacot et al., 2018). An efficient algorithm to compute the NTK, as well as its convolutional counterparts, appears in Arora et al. (2019a), which allowed studying performance of infinitely wide nets on datasets like CIFAR-10. However, super-quadratic running time of kernel methods makes them best suited for small-data tasks. We report results suggesting neural tangent kernels perform strongly on low-data tasks. 1. On a standard testbed of classification/regression tasks from the UCI database, NTK SVM beats the previous gold standard, Random Forests (RF), and also the corresponding finite nets. 2. On CIFAR-10 with 10 - 640 training samples, Convolutional NTK consistently beats ResNet-34 by 1% - 3%. 3. On VOC07 testbed for few-shot image classification tasks on ImageNet with transfer learning (Goyal et al., 2019), replacing the linear SVM currently used with a Convolutional NTK SVM consistently improves performance. 4. Comparing the performance of NTK with the finite-width net it was derived from, NTK behavior starts at lower net widths than suggested by theoretical analysis(Arora et al., 2019a). NTK's efficacy may trace to lower variance of output.
We propose a novel method to train deep convolutional neural networks which learn from multiple data sets of varying input sizes through weight sharing. This is an advantage in chemometrics where individual measurements represent exact chemical compounds and thus signals cannot be translated or resized without disturbing their interpretation. Our approach show superior performance compared to transfer learning when a medium sized and a small data set are trained together. While we observe a small improvement compared to individual training when two medium sized data sets are trained together, in particular through a reduction in the variance.
Generative classifiers offer potential advantages over their discriminative counterparts, namely in the areas of data efficiency, robustness to data shift and adversarial examples, and zero-shot learning (Ng and Jordan,2002; Yogatama et al., 2017; Lewis and Fan,2019). In this paper, we improve generative text classifiers by introducing discrete latent variables into the generative story, and explore several graphical model configurations. We parameterize the distributions using standard neural architectures used in conditional language modeling and perform learning by directly maximizing the log marginal likelihood via gradient-based optimization, which avoids the need to do expectation-maximization. We empirically characterize the performance of our models on six text classification datasets. The choice of where to include the latent variable has a significant impact on performance, with the strongest results obtained when using the latent variable as an auxiliary conditioning variable in the generation of the textual input. This model consistently outperforms both the generative and discriminative classifiers in small-data settings. We analyze our model by using it for controlled generation, finding that the latent variable captures interpretable properties of the data, even with very small training sets.
Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree. While effective for relatively short-term time integration, when long time integration of the time-dependent PDEs is sought, the time-space domain may become arbitrarily large and hence training of the neural network may become prohibitively expensive. To this end, we develop a parareal physics-informed neural network (PPINN), hence decomposing a long-time problem into many independent short-time problems supervised by an inexpensive/fast coarse-grained (CG) solver. In particular, the serial CG solver is designed to provide approximate predictions of the solution at discrete times, while initiate many fine PINNs simultaneously to correct the solution iteratively. There is a two-fold benefit from training PINNs with small-data sets rather than working on a large-data set directly, i.e., training of individual PINNs with small-data is much faster, while training the fine PINNs can be readily parallelized. Consequently, compared to the original PINN approach, the proposed PPINN approach may achieve a significant speedup for long-time integration of PDEs, assuming that the CG solver is fast and can provide reasonable predictions of the solution, hence aiding the PPINN solution to converge in just a few iterations. To investigate the PPINN performance on solving time-dependent PDEs, we first apply the PPINN to solve the Burgers equation, and subsequently we apply the PPINN to solve a two-dimensional nonlinear diffusion-reaction equation. Our results demonstrate that PPINNs converge in a couple of iterations with significant speed-ups proportional to the number of time-subdomains employed.
Discovering oral cavity cancer (OCC) at an early stage is an effective way to increase patient survival rate. However, current initial screening process is done manually and is expensive for the average individual, especially in developing countries worldwide. This problem is further compounded due to the lack of specialists in such areas. Automating the initial screening process using artificial intelligence (AI) to detect pre-cancerous lesions can prove to be an effective and inexpensive technique that would allow patients to be triaged accordingly to receive appropriate clinical management. In this study, we have applied and evaluated the efficacy of six deep convolutional neural network (DCNN) models using transfer learning, for identifying pre-cancerous tongue lesions directly using a small data set of clinically annotated photographic images to diagnose early signs of OCC. DCNN model based on Vgg19 architecture was able to differentiate between benign and pre-cancerous tongue lesions with a mean classification accuracy of 0.98, sensitivity 0.89 and specificity 0.97. Additionally, the ResNet50 DCNN model was able to distinguish between five types of tongue lesions i.e. hairy tongue, fissured tongue, geographic tongue, strawberry tongue and oral hairy leukoplakia with a mean classification accuracy of 0.97. Preliminary results using an (AI+Physician) ensemble model demonstrate that an automated initial screening process of tongue lesions using DCNNs can achieve near-human level classification performance for diagnosing early signs of OCC in patients.
Standard autoregressive seq2seq models are easily trained by max-likelihood, but tend to show poor results under small-data conditions. We introduce a class of seq2seq models, GAMs (Global Autoregressive Models), which combine an autoregressive component with a log-linear component, allowing the use of global \textit{a priori} features to compensate for lack of data. We train these models in two steps. In the first step, we obtain an \emph{unnormalized} GAM that maximizes the likelihood of the data, but is improper for fast inference or evaluation. In the second step, we use this GAM to train (by distillation) a second autoregressive model that approximates the \emph{normalized} distribution associated with the GAM, and can be used for fast inference and evaluation. Our experiments focus on language modelling under synthetic conditions and show a strong perplexity reduction of using the second autoregressive model over the standard one.
Increasing volume of Electronic Health Records (EHR) in recent years provides great opportunities for data scientists to collaborate on different aspects of healthcare research by applying advanced analytics to these EHR clinical data. A key requirement however is obtaining meaningful insights from high dimensional, sparse and complex clinical data. Data science approaches typically address this challenge by performing feature learning in order to build more reliable and informative feature representations from clinical data followed by supervised learning. In this paper, we propose a predictive modeling approach based on deep learning based feature representations and word embedding techniques. Our method uses different deep architectures (stacked sparse autoencoders, deep belief network, adversarial autoencoders and variational autoencoders) for feature representation in higher-level abstraction to obtain effective and robust features from EHRs, and then build prediction models on top of them. Our approach is particularly useful when the unlabeled data is abundant whereas labeled data is scarce. We investigate the performance of representation learning through a supervised learning approach. Our focus is to present a comparative study to evaluate the performance of different deep architectures through supervised learning and provide insights in the choice of deep feature representation techniques. Our experiments demonstrate that for small data sets, stacked sparse autoencoder demonstrates a superior generality performance in prediction due to sparsity regularization whereas variational autoencoders outperform the competing approaches for large data sets due to its capability of learning the representation distribution
It is well-known that overparametrized neural networks trained using gradient-based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly overparametrized networks under reasonable assumptions. These results either assume that the activation function is ReLU or they crucially depend on the minimum eigenvalue of a certain Gram matrix depending on the data, random initialization and the activation function. In the later case, existing works only prove that this minimum eigenvalue is non-zero and do not provide quantitative bounds. On the empirical side, a contemporary line of investigations has proposed a number of alternative activation functions which tend to perform better than ReLU at least in some settings but no clear understanding has emerged. This state of affairs underscores the importance of theoretically understanding the impact of activation functions on training. In the present paper, we provide theoretical results about the effect of activation function on the training of highly overparametrized 2-layer neural networks. A crucial property that governs the performance of an activation is whether or not it is smooth. For non-smooth activations such as ReLU, SELU and ELU, all eigenvalues of the associated Gram matrix are large under minimal assumptions on the data. For smooth activations such as tanh, swish and polynomials, the situation is more complex. If the subspace spanned by the data has small dimension then the minimum eigenvalue of the Gram matrix can be small leading to slow training. But if the dimension is large and the data satisfies another mild condition, then the eigenvalues are large. If we allow deep networks, then the small data dimension is not a limitation provided that the depth is sufficient. We discuss a number of extensions and applications of these results.
High entropy alloys (HEAs) have been increasingly attractive as promising next-generation materials due to their various excellent properties. It's necessary to essentially characterize the degree of chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed and demonstrated on the accurate and efficient prediction of configurational energy of high entropy alloys. The proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. Given limited data calculated by first-principles calculations, Bayesian regularized regression not only offers an accurate and stable prediction but also effectively quantifies the uncertainties associated with EPI parameters. Compared with the arbitrary determination of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence we can place in statistical estimates of configurational energy when data are sparse.
The claims that big data holds the key to enterprise successes and that Artificial Intelligence is going to replace humanity have become increasingly more popular over the past few years, both in academia and in the industry. However, while these claims may indeed capture some truth, they have also been massively oversold, or so we contend here. The goal of this paper is two-fold. First, we provide a qualified defence of the value of less data within the context of AI. This is done by carefully reviewing two distinct problems for big data driven AI, namely a) the limited track record of Deep Learning in key areas such as Natural Language Processing, b) the regulatory and business significance of being able to learn from few data points. Second, we briefly sketch what we refer to as a case of AI with humans and for humans, namely an AI paradigm whereby the systems we build are privacy-oriented and focused on human-machine collaboration, not competition. Combining our claims above, we conclude that when seen through the lens of cognitively inspired AI, the bright future of the discipline is about less data, not more, and more humans, not fewer.
Different agents need to make a prediction. They observe identical data, but have different models: they predict using different explanatory variables. We study which agent believes they have the best predictive ability -- as measured by the smallest subjective posterior mean squared prediction error -- and show how it depends on the sample size. With small samples, we present results suggesting it is an agent using a low-dimensional model. With large samples, it is generally an agent with a high-dimensional model, possibly including irrelevant variables, but never excluding relevant ones. We apply our results to characterize the winning model in an auction of productive assets, to argue that entrepreneurs and investors with simple models will be over-represented in new sectors, and to understand the proliferation of "factors" that explain the cross-sectional variation of expected stock returns in the asset-pricing literature.
Missing data are unavoidable in wireless sensor networks, due to issues such as network communication outage, sensor maintenance or failure, etc. Although a plethora of methods have been proposed for imputing sensor data, limitations still exist. Firstly, most methods give poor estimates when a consecutive number of data are missing. Secondly, some methods reconstruct missing data based on other parameters monitored simultaneously. When all the data are missing, these methods are no longer effective. Thirdly, the performance of deep learning methods relies highly on a massive number of training data. Moreover in many scenarios, it is difficult to obtain large volumes of data from wireless sensor networks. Hence, we propose a new sequence-to-sequence imputation model (SSIM) for recovering missing data in wireless sensor networks. The SSIM uses the state-of-the-art sequence-to-sequence deep learning architecture, and the Long Short Term Memory Network is chosen to utilize both the past and future information for a given time. Moreover, a variable-length sliding window algorithm is developed to generate a large number of training samples so the SSIM can be trained with small data sets. We evaluate the SSIM by using real-world time series data from a water quality monitoring network. Compared to methods like ARIMA, Seasonal ARIMA, Matrix Factorization, Multivariate Imputation by Chained Equations and Expectation Maximization, the proposed SSIM achieves up to 69.2%, 70.3%, 98.3% and 76% improvements in terms of the RMSE, MAE, MAPE and SMAPE respectively, when recovering missing data sequences of three different lengths. The SSIM is therefore a promising approach for data quality control in wireless sensor networks.
End-to-end automatic speech recognition (ASR) models are increasingly large and complex to achieve the best possible accuracy. In this paper, we build an AutoML system that uses reinforcement learning (RL) to optimize the per-layer compression ratios when applied to a state-of-the-art attention based end-to-end ASR model composed of several LSTM layers. We use singular value decomposition (SVD) low-rank matrix factorization as the compression method. For our RL-based AutoML system, we focus on practical considerations such as the choice of the reward/punishment functions, the formation of an effective search space, and the creation of a representative but small data set for quick evaluation between search steps. Finally, we present accuracy results on LibriSpeech of the model compressed by our AutoML system, and we compare it to manually-compressed models. Our results show that in the absence of retraining our RL-based search is an effective and practical method to compress a production-grade ASR system. When retraining is possible, we show that our AutoML system can select better highly-compressed seed models compared to manually hand-crafted rank selection, thus allowing for more compression than previously possible.
In the recent years, convolutional neural networks have transformed the field of medical image analysis due to their capacity to learn discriminative image features for a variety of classification and regression tasks. However, successfully learning these features requires a large amount of manually annotated data, which is expensive to acquire and limited by the available resources of expert image analysts. Therefore, unsupervised, weakly-supervised and self-supervised feature learning techniques receive a lot of attention, which aim to utilise the vast amount of available data, while at the same time avoid or substantially reduce the effort of manual annotation. In this paper, we propose a novel way for training a cardiac MR image segmentation network, in which features are learnt in a self-supervised manner by predicting anatomical positions. The anatomical positions serve as a supervisory signal and do not require extra manual annotation. We demonstrate that this seemingly simple task provides a strong signal for feature learning and with self-supervised learning, we achieve a high segmentation accuracy that is better than or comparable to a U-net trained from scratch, especially at a small data setting. When only five annotated subjects are available, the proposed method improves the mean Dice metric from 0.811 to 0.852 for short-axis image segmentation, compared to the baseline U-net.
Compared to 2D face presentation attacks (e.g. printed photos and video replays), 3D type attacks are more challenging to face recognition systems (FRS) by presenting 3D characteristics or materials similar to real faces. Existing 3D face spoofing databases, however, mostly based on 3D masks, are restricted to small data size or poor authenticity due to the production difficulty and high cost. In this work, we introduce the first wax figure face database, WFFD, as one type of super-realistic 3D presentation attacks to spoof the FRS. This database consists of 2200 images with both real and wax figure faces (totally 4400 faces) with a high diversity from online collections. Experiments on this database first investigate the vulnerability of three popular FRS to this kind of new attack. Further, we evaluate the performance of several face presentation attack detection methods to show the attack abilities of this super-realistic face spoofing database.
We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of the sliced inverse regression (SIR) and the sliced average variance estimation (SAVE) type of methods, which is to use the statistical information of the conditional distribution $\pi(\-x|y)$ to identify the dimension reduction (DR) space. In particular we focus on the task of computing this conditional distribution without slicing the data. We propose a Bayesian framework to compute the conditional distribution where the likelihood function is obtained using the Gaussian process regression model. The conditional distribution $\pi(\-x|y)$ can then be computed directly via Monte Carlo sampling. We then can perform DR by considering certain moment functions (e.g. the first or the second moment) of the samples of the posterior distribution. With numerical examples, we demonstrate that the proposed method is especially effective for small data problems.
There has been recent interest in improving performance of simple models for multiple reasons such as interpretability, robust learning from small data, deployment in memory constrained settings as well as environmental considerations. In this paper, we propose a novel method SRatio that can utilize information from high performing complex models (viz. deep neural networks, boosted trees, random forests) to reweight a training dataset for a potentially low performing simple model of much lower complexity such as a decision tree or a shallow network enhancing its performance. Our method also leverages the per sample hardness estimate of the simple model which is not the case with the prior works which primarily consider the complex model's confidences/predictions and is thus conceptually novel. Moreover, we generalize and formalize the concept of attaching probes to intermediate layers of a neural network to other commonly used classifiers and incorporate this into our method. The benefit of these contributions is witnessed in the experiments where on 6 UCI datasets and CIFAR-10 we outperform competitors in a majority (16 out of 27) of the cases and tie for best performance in the remaining cases. In fact, in a couple of cases, we even approach the complex model's performance. We also conduct further experiments to validate assertions and intuitively understand why our method works. Theoretically, we motivate our approach by showing that the weighted loss minimized by simple models using our weighting upper bounds the loss of the complex model.
In this paper, we present Hitachi and Paderborn University's joint effort for automatic speech recognition (ASR) in a dinner party scenario. The main challenges of ASR systems for dinner party recordings obtained by multiple microphone arrays are (1) heavy speech overlaps, (2) severe noise and reverberation, (3) very natural conversational content, and possibly (4) insufficient training data. As an example of a dinner party scenario, we have chosen the data presented during the CHiME-5 speech recognition challenge, where the baseline ASR had a 73.3% word error rate (WER), and even the best performing system at the CHiME-5 challenge had a 46.1% WER. We extensively investigated a combination of the guided source separation-based speech enhancement technique and an already proposed strong ASR backend and found that a tight combination of these techniques provided substantial accuracy improvements. Our final system achieved WERs of 39.94% and 41.64% for the development and evaluation data, respectively, both of which are the best published results for the dataset. We also investigated with additional training data on the official small data in the CHiME-5 corpus to assess the intrinsic difficulty of this ASR task.
As the application of deep learning has expanded to real-world problems with insufficient volume of training data, transfer learning recently has gained much attention as means of improving the performance in such small-data regime. However, when existing methods are applied between heterogeneous architectures and tasks, it becomes more important to manage their detailed configurations and often requires exhaustive tuning on them for the desired performance. To address the issue, we propose a novel transfer learning approach based on meta-learning that can automatically learn what knowledge to transfer from the source network to where in the target network. Given source and target networks, we propose an efficient training scheme to learn meta-networks that decide (a) which pairs of layers between the source and target networks should be matched for knowledge transfer and (b) which features and how much knowledge from each feature should be transferred. We validate our meta-transfer approach against recent transfer learning methods on various datasets and network architectures, on which our automated scheme significantly outperforms the prior baselines that find "what and where to transfer" in a hand-crafted manner.
We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their derivatives. A neural network approximates the data and constructs the function library, but it also performs the sparse regression. This construction makes it extremely robust to noise, applicable to small data sets, and, contrary to other deep learning methods, does not require a training set. We benchmark our approach on several physical problems such as the Burgers', Korteweg-de Vries and Keller-Segel equations, and find that it requires as few as $\mathcal{O}(10^2)$ samples and works at noise levels up to $75\%$. Motivated by these results, we apply DeepMoD directly on noisy experimental time-series data from a gel electrophoresis experiment and find that it discovers the advection-diffusion equation describing this system.