Statistical analysis (SA) is a complex process to deduce population properties from analysis of data. It usually takes a well-trained analyst to successfully perform SA, and it becomes extremely challenging to apply SA to big data applications. We propose to use deep neural networks to automate the SA process. In particular, we propose to construct convolutional neural networks (CNNs) to perform automatic model selection and parameter estimation, two most important SA tasks. We refer to the resulting CNNs as the neural model selector and the neural model estimator, respectively, which can be properly trained using labeled data systematically generated from candidate models. Simulation study shows that both the selector and estimator demonstrate excellent performances. The idea and proposed framework can be further extended to automate the entire SA process and have the potential to revolutionize how SA is performed in big data analytics.

Research from a variety of fields including psychology and linguistics have found correlations and patterns in personal attributes and behavior, but efforts to understand the broader heterogeneity in human behavior have not yet integrated these approaches and perspectives with a cohesive methodology. Here we extract patterns in behavior and relate those patterns together in a high-dimensional picture. We use dimension reduction to analyze word usage in text data from the online discussion platform Reddit. We find that pronouns can be used to characterize the space of the two most prominent dimensions that capture the greatest differences in word usage, even though pronouns were not included in the determination of those dimensions. These patterns overlap with patterns of topics of discussion to reveal relationships between pronouns and topics that can describe the user population. This analysis corroborates findings from past research that have identified word use differences across populations and synthesizes them relative to one another. We believe this is a step toward understanding how differences between people are related to each other.

Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very hard to be parallelized, specially with very large matrices. In this paper, we introduce a new method for collaborative filtering based on Matrix Factorization by combining simulated annealing with levy distribution. By using this method, good solutions are achieved in acceptable time with low computations, compared to other methods like stochastic gradient descent, alternating least squares, and weighted non-negative matrix factorization.

We propose a novel architecture for $k$-shot classification on the Omniglot dataset. Building on prototypical networks, we extend their architecture to what we call Gaussian prototypical networks. Prototypical networks learn a map between images and embedding vectors, and use their clustering for classification. In our model, a part of the encoder output is interpreted as a confidence region estimate about the embedding point, and expressed as a Gaussian covariance matrix. Our network then constructs a direction and class dependent distance metric on the embedding space, using uncertainties of individual data points as weights. We show that Gaussian prototypical networks are a preferred architecture over vanilla prototypical networks with an equivalent number of parameters. We report state-of-the-art performance in 1-shot and 5-shot classification both in 5-way and 20-way regime (for 5-shot 5-way, we are comparable to previous state-of-the-art) on the Omniglot dataset. We explore artificially down-sampling a fraction of images in the training set, which improves our performance even further. We therefore hypothesize that Gaussian prototypical networks might perform better in less homogeneous, noisier datasets, which are commonplace in real world applications.

Many stochastic optimization algorithms work by estimating the gradient of the cost function on the fly by sampling datapoints uniformly at random from a training set. However, the estimator might have a large variance, which inadvertently slows down the convergence rate of the algorithms. One way to reduce this variance is to sample the datapoints from a carefully selected non-uniform distribution. In this work, we propose a novel non-uniform sampling approach that uses the multi-armed bandit framework. Theoretically, we show that our algorithm asymptotically approximates the optimal variance within a factor of 3. Empirically, we show that using this datapoint-selection technique results in a significant reduction in the convergence time and variance of several stochastic optimization algorithms such as SGD, SVRG and SAGA. This approach for sampling datapoints is general, and can be used in conjunction with any algorithm that uses an unbiased gradient estimation -- we expect it to have broad applicability beyond the specific examples explored in this work.

Noisy PN learning is the problem of binary classification when training examples may be mislabeled (flipped) uniformly with noise rate rho1 for positive examples and rho0 for negative examples. We propose Rank Pruning (RP) to solve noisy PN learning and the open problem of estimating the noise rates, i.e. the fraction of wrong positive and negative labels. Unlike prior solutions, RP is time-efficient and general, requiring O(T) for any unrestricted choice of probabilistic classifier with T fitting time. We prove RP has consistent noise estimation and equivalent expected risk as learning with uncorrupted labels in ideal conditions, and derive closed-form solutions when conditions are non-ideal. RP achieves state-of-the-art noise estimation and F1, error, and AUC-PR for both MNIST and CIFAR datasets, regardless of the amount of noise and performs similarly impressively when a large portion of training examples are noise drawn from a third distribution. To highlight, RP with a CNN classifier can predict if an MNIST digit is a "one"or "not" with only 0.25% error, and 0.46 error across all digits, even when 50% of positive examples are mislabeled and 50% of observed positive labels are mislabeled negative examples.

Recent literature on deep neural networks for tagging of highly energetic jets resulting from top quark decays has focused on image based techniques or multivariate approaches using high-level jet substructure variables. Here, a sequential approach to this task is taken by using an ordered sequence of jet constituents as training inputs. Unlike the majority of previous approaches, this strategy does not result in a loss of information during pixelisation or the calculation of high level features. The jet classification method achieves a background rejection of 45 at a 50% efficiency operating point for reconstruction level jets with transverse momentum range of 600 to 2500 GeV and is insensitive to multiple proton-proton interactions at the levels expected throughout Run 2 of the LHC.

Noise injection (NI) is an approach to mitigate over-fitting in feedforward neural networks (NNs). The Bernoulli NI procedure as implemented in dropout and shakeout has connections with $l_1$ and $l_2$ regularization on the NN model parameters and demonstrates the efficiency and feasibility of NI in regularizing NNs. We propose whiteout, a new NI regularization technique with adaptive Gaussian noise in NNs. Whiteout is more versatile than dropout and shakeout. We show that the optimization objective function associated with whiteout in generalized linear models has a closed-form penalty term that has connections with a wide range of regularization and includes the bridge, lasso, ridge, and elastic net penalization as special cases; it can be also extended to offer regularization similar to the adaptive lasso and group lasso. We prove that whiteout can also be viewed as robust learning of NNs in the presence of small perturbations in input and hidden nodes. We establish that the noise-perturbed empirical loss function with whiteout converges almost surely to the ideal loss function, and the estimates of NN parameters obtained from minimizing the former loss function are consistent with those obtained from minimizing the ideal loss function. Computationally, whiteout can be easily incorporated in the back-propagation algorithm. The superiority of whiteout over dropout and shakeout in learning NNs with relatively small sized training data is demonstrated using the the LSVT voice rehabilitation data and the LIBRAS hand movement data.

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^\alpha)$ disjoint subsets. On each subset, some spectral regularization method (belonging to a large class, including in particular Kernel Ridge Regression, $L^2$-boosting and spectral cut-off) is applied. The regression function $f$ is then estimated via simple averaging, leading to a substantial reduction in computation time. We show that minimax optimal rates of convergence are preserved if m grows sufficiently slowly (corresponding to an upper bound for $\alpha$) as $n \to \infty$, depending on the smoothness assumptions on $f$ and the intrinsic dimensionality. In spirit, our approach is classical.

We investigate the problem of learning representations that are invariant to certain nuisance or sensitive factors of variation in the data while retaining as much of the remaining information as possible. Our model is based on a variational autoencoding architecture (Kingma & Welling, 2014; Rezende et al., 2014) with priors that encourage independence between sensitive and latent factors of variation. Any subsequent processing, such as classification, can then be performed on this purged latent representation. To remove any remaining dependencies we incorporate an additional penalty term based on the "Maximum Mean Discrepancy" (MMD) (Gretton et al., 2006) measure. We discuss how these architectures can be efficiently trained on data and show in experiments that this method is more effective than previous work in removing unwanted sources of variation while maintaining informative latent representations. In "Representation Learning" one tries to find representations of the data that are informative for a particular task while removing the factors of variation that are uninformative and are typically detrimental for the task under consideration. Uninformative dimensions are often called "noise" or "nuisance variables" while informative dimensions are usually called latent or hidden factors of variation.