Building a scalable machine learning system for unsupervised anomaly detection via representation learning is highly desirable. One of the prevalent methods is using a reconstruction error from variational autoencoder (VAE) via maximizing the evidence lower bound. We revisit VAE from the perspective of information theory to provide some theoretical foundations on using the reconstruction error, and finally arrive at a simpler and more effective model for anomaly detection. In addition, to enhance the effectiveness of detecting anomalies, we incorporate a practical model uncertainty measure into the metric. We show empirically the competitive performance of our approach on benchmark datasets.

Signal models based on sparse representation have received considerable attention in recent years. Compared to synthesis dictionary learning, sparsifying transform learning involves highly efficient sparse coding and operator update steps. In this work, we propose a Multi-layer Residual Sparsifying Transform (MRST) learning model wherein the transform domain residuals are jointly sparsified over layers. In particular, the transforms for the deeper layers exploit the more intricate properties of the residual maps. We investigate the application of the learned MRST model for low-dose CT reconstruction using Penalized Weighted Least Squares (PWLS) optimization. Experimental results on Mayo Clinic data show that the MRST model outperforms conventional methods such as FBP and PWLS methods based on edge-preserving (EP) regularizer and single-layer transform (ST) model, especially for maintaining some subtle details.

In the field of numerical weather prediction (NWP), the probabilistic distribution of the future state of the atmosphere is sampled with Monte-Carlo-like simulations, called ensembles. These ensembles have deficiencies (such as conditional biases) that can be corrected thanks to statistical post-processing methods. Several ensembles exist and may be corrected with different statistiscal methods. A further step is to combine these raw or post-processed ensembles. The theory of prediction with expert advice allows us to build combination algorithms with theoretical guarantees on the forecast performance. This article adapts this theory to the case of probabilistic forecasts issued as step-wise cumulative distribution functions (CDF). The theory is applied to wind speed forecasting, by combining several raw or post-processed ensembles, considered as CDFs. The second goal of this study is to explore the use of two forecast performance criteria: the Continous ranked probability score (CRPS) and the Jolliffe-Primo test. Comparing the results obtained with both criteria leads to reconsidering the usual way to build skillful probabilistic forecasts, based on the minimization of the CRPS. Minimizing the CRPS does not necessarily produce reliable forecasts according to the Jolliffe-Primo test. The Jolliffe-Primo test generally selects reliable forecasts, but could lead to issuing suboptimal forecasts in terms of CRPS. It is proposed to use both criterion to achieve reliable and skillful probabilistic forecasts.

Recent state-of-the-art autoencoder based generative models have an encoder-decoder structure and learn a latent representation with a pre-defined distribution that can be sampled from. Implementing the encoder networks of these models in a stochastic manner provides a natural and common approach to avoid overfitting and enforce a smooth decoder function. However, we show that for stochastic encoders, simultaneously attempting to enforce a distribution constraint and minimising an output distortion leads to a reduction in generative and reconstruction quality. In addition, attempting to enforce a latent distribution constraint is not reasonable when performing disentanglement. Hence, we propose the variance-constrained autoencoder (VCAE), which only enforces a variance constraint on the latent distribution. Our experiments show that VCAE improves upon Wasserstein Autoencoder and the Variational Autoencoder in both reconstruction and generative quality on MNIST and CelebA. Moreover, we show that VCAE equipped with a total correlation penalty term performs equivalently to FactorVAE at learning disentangled representations on 3D-Shapes while being a more principled approach.

Optical Character Recognition and extraction is a key tool in the automatic evaluation of documents in a financial context. However, the image data provided to automated systems can have unreliable quality, and can be inherently low-resolution or downsampled and compressed by a transmitting program. In this paper, we illustrate the efficacy of a Gaussian Process upsampling model for the purposes of improving OCR and extraction through upsampling low resolution documents.

This paper considers the problem of estimation of the Fisher information for location from a random sample of size $n$. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new estimator, termed a clipped estimator, is proposed. Superior upper bounds on the rates of convergence can be shown for the new estimator compared to the Bhattacharya estimator, albeit with different regularity conditions. Third, both of the estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown's identity, which relates the Fisher information and the minimum mean squared error (MMSE) in Gaussian noise, two corresponding consistent estimators for the MMSE are proposed. Simulation examples for the Bhattacharya estimator and the clipped estimator as well as the MMSE estimators are presented. The examples demonstrate that the clipped estimator can significantly reduce the required sample size to guarantee a specific confidence interval compared to the Bhattacharya estimator.

Planning is a powerful approach to control problems with known environment dynamics. In unknown environments the agent needs to learn a model of the system dynamics to make planning applicable. This is particularly challenging when the underlying states are only indirectly observable through images. We propose to learn a deep latent Gaussian process dynamics (DLGPD) model that learns low-dimensional system dynamics from environment interactions with visual observations. The method infers latent state representations from observations using neural networks and models the system dynamics in the learned latent space with Gaussian processes. All parts of the model can be trained jointly by optimizing a lower bound on the likelihood of transitions in image space. We evaluate the proposed approach on the pendulum swing-up task while using the learned dynamics model for planning in latent space in order to solve the control problem. We also demonstrate that our method can quickly adapt a trained agent to changes in the system dynamics from just a few rollouts. We compare our approach to a state-of-the-art purely deep learning based method and demonstrate the advantages of combining Gaussian processes with deep learning for data efficiency and transfer learning.

The transfer learning technique is widely used to learning in one context and applying it to another, i.e. the capacity to apply acquired knowledge and skills to new situations. But is it possible to transfer the learning from a deep neural network to a weaker neural network? Is it possible to improve the performance of a weak neural network using the knowledge acquired by a more powerful neural network? In this work, during the training process of a weak network, we add a loss function that minimizes the distance between the features previously learned from a strong neural network with the features that the weak network must try to learn. To demonstrate the effectiveness and robustness of our approach, we conducted a large number of experiments using three known datasets and demonstrated that a weak neural network can increase its performance if its learning process is driven by a more powerful neural network.

The notion of incremental learning is to train an ANN algorithm in stages, as and when newer training data arrives. Incremental learning is becoming widespread in recent times with the advent of deep learning. Noise in the training data reduces the accuracy of the algorithm. In this paper, we make an empirical study of the effect of noise in the training phase. We numerically show that the accuracy of the algorithm is dependent more on the location of the error than the percentage of error. Using Perceptron, Feed Forward Neural Network and Radial Basis Function Neural Network, we show that for the same percentage of error, the accuracy of the algorithm significantly varies with the location of error. Furthermore, our results show that the dependence of the accuracy with the location of error is independent of the algorithm.

The large bulk of work in multiple testing has focused on specifying procedures that control the false discovery rate (FDR), with relatively less attention being paid to the corresponding Type II error known as the false non-discovery rate (FNR). A line of more recent work in multiple testing has begun to investigate the tradeoffs between the FDR and FNR and to provide lower bounds on the performance of procedures that depend on the model structure. Lacking thus far, however, has been a general approach to obtaining lower bounds for a broad class of models. This paper introduces an analysis strategy based on derandomization, illustrated by applications to various concrete models. Our main result is meta-theorem that gives a general recipe for obtaining lower bounds on the combination of FDR and FNR. We illustrate this meta-theorem by deriving explicit bounds for several models, including instances with dependence, scale-transformed alternatives, and non-Gaussian-like distributions. We provide numerical simulations of some of these lower bounds, and show a close relation to the actual performance of the Benjamini-Hochberg (BH) algorithm.