We study deep neural networks and their use in semiparametric inference. We provide new rates of convergence for deep feedforward neural nets and, because our rates are sufficiently fast (in some cases minimax optimal), prove that semiparametric inference is valid using deep nets for first-step estimation. Our estimation rates and semiparametric inference results are the first in the literature to handle the current standard architecture: fully connected feedforward neural networks (multi-layer perceptrons), with the now-default rectified linear unit (ReLU) activation function and a depth explicitly diverging with the sample size. We discuss other architectures as well, including fixed-width, very deep networks. We establish nonasymptotic bounds for these deep ReLU nets, for both least squares and logistic loses in nonparametric regression. We then apply our theory to develop semiparametric inference, focusing on treatment effects and expected profits for concreteness, and demonstrate their effectiveness with an empirical application to direct mail marketing. Inference in many other semiparametric contexts can be readily obtained.

Network representation aims to represent the nodes in a network as continuous and compact vectors, and has attracted much attention in recent years due to its ability to capture complex structure relationships inside networks. However, existing network representation methods are commonly designed for homogeneous information networks where all the nodes (entities) of a network are of the same type, e.g., papers in a citation network. In this paper, we propose a universal network representation approach (UNRA), that represents different types of nodes in heterogeneous information networks in a continuous and common vector space. The UNRA is built on our latest mutually updated neural language module, which simultaneously captures inter-relationship among homogeneous nodes and node-content correlation. Relationships between different types of nodes are also assembled and learned in a unified framework. Experiments validate that the UNRA achieves outstanding performance, compared to six other state-of-the-art algorithms, in node representation, node classification, and network visualization. In node classification, the UNRA achieves a 3\% to 132\% performance improvement in terms of accuracy.

Grammatical error correction, like other machine learning tasks, greatly benefits from large quantities of high quality training data, which is typically expensive to produce. While writing a program to automatically generate realistic grammatical errors would be difficult, one could learn the distribution of naturallyoccurring errors and attempt to introduce them into other datasets. Initial work on inducing errors in this way using statistical machine translation has shown promise; we investigate cheaply constructing synthetic samples, given a small corpus of human-annotated data, using an off-the-rack attentive sequence-to-sequence model and a straight-forward post-processing procedure. Our approach yields error-filled artificial data that helps a vanilla bi-directional LSTM to outperform the previous state of the art at grammatical error detection, and a previously introduced model to gain further improvements of over 5% $F_{0.5}$ score. When attempting to determine if a given sentence is synthetic, a human annotator at best achieves 39.39 $F_1$ score, indicating that our model generates mostly human-like instances.

Abstract--This paper explores using a Long short-term memory (LSTM) based sequence autoencoder to learn interesting features for detecting surveillance aircraft using ADS-B flight data. An aircraft periodically broadcasts ADS-B (Automatic Dependent Surveillance - Broadcast) data to ground receivers. The ability of LSTM networks to model varying length time series data and remember dependencies that span across events makes it an ideal candidate for implementing a sequence autoencoder for ADS-B data because of its possible variable length time series, irregular sampling and dependencies that span across events. The motivation for this research was inspired by the original research presented by Richards, MacDonald-Evoy, and Hernandez in their "Tracking Spies In The Skies" talk at DEF CON 25 [1]. The goal of their research is to leverage ADS-B (Automatic Dependent Surveillance - Broadcast) data that is broadcast by commercial and private aircraft to detect surveillance aircraft.

Recently, generative adversarial networks have gained a lot of popularity for image generation tasks. However, such models are associated with complex learning mechanisms and demand very large relevant datasets. This work borrows concepts from image and video captioning models to form an image generative framework. The model is trained in a similar fashion as recurrent captioning model and uses the learned weights for image generation. This is done in an inverse direction, where the input is a caption and the output is an image. The vector representation of the sentence and frames are extracted from an encoder-decoder model which is initially trained on similar sentence and image pairs. Our model conditions image generation on a natural language caption. We leverage a sequence-to-sequence model to generate synthetic captions that have the same meaning for having a robust image generation. One key advantage of our method is that the traditional image captioning datasets can be used for synthetic sentence paraphrases. Results indicate that images generated through multiple captions are better at capturing the semantic meaning of the family of captions.

Gradient control plays an important role in feed-forward networks applied to various computer vision tasks. Previous work has shown that Recurrent Highway Networks minimize the problem of vanishing or exploding gradients. They achieve this by setting the eigenvalues of the temporal Jacobian to 1 across the time steps. In this work, batch normalized recurrent highway networks are proposed to control the gradient flow in an improved way for network convergence. Specifically, the introduced model can be formed by batch normalizing the inputs at each recurrence loop. The proposed model is tested on an image captioning task using MSCOCO dataset. Experimental results indicate that the batch normalized recurrent highway networks converge faster and performs better compared with the traditional LSTM and RHN based models.

We study two types of preconditioners and preconditioned stochastic gradient descent (SGD) methods in a unified framework. We call the first one the Newton type due to its close relationship to Newton method, and the second one the Fisher type as its preconditioner is closely related to the inverse of Fisher information matrix. Both preconditioners can be derived from one framework, and efficiently learned on any matrix Lie groups designated by the user using natural or relative gradient descent. Many existing preconditioners and methods are special cases of either the Newton type or the Fisher type ones. Experimental results on relatively large scale machine learning problems are reported for performance study.

We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Amp\`ere flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Amp\`ere equation, optimal transport, and fluid dynamics into reversible flow-based generative models.

We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models constructed in our framework assign probabilities to uncertain realizations, leading to Kullback-Leibler Divergence (KLD) as the linear layer. In our model construction, we also arrive at a structure similar to ReLU activation supported with Bayes' theorem. The non-linearities in our framework are normalization layers with ReLU and Sigmoid as element-wise approximations. Additionally, the pooling function is derived as a marginalization of spatial random variables according to the mechanics of the framework. As such, Max Pooling is an approximation to the aforementioned marginalization process. Since our models are comprised of finite state distributions (FSD) as variables and parameters, exact computation of information-theoretic quantities such as entropy and KLD is possible, thereby providing more objective measures to analyze networks. Unlike existing designs that rely on heuristics, the proposed framework restricts subjective interpretations of CNNs and sheds light on the functionality of neural networks from a completely new perspective.

Trust region and cubic regularization methods have demonstrated good performance in small scale non-convex optimization, showing the ability to escape from saddle points. Each iteration of these methods involves computation of gradient, Hessian and function value in order to obtain the search direction and adjust the radius or cubic regularization parameter. However, exactly computing those quantities are too expensive in large-scale problems such as training deep networks. In this paper, we study a family of stochastic trust region and cubic regularization methods when gradient, Hessian and function values are computed inexactly, and show the iteration complexity to achieve $\epsilon$-approximate second-order optimality is in the same order with previous work for which gradient and function values are computed exactly. The mild conditions on inexactness can be achieved in finite-sum minimization using random sampling. We show the algorithm performs well on training convolutional neural networks compared with previous second-order methods.