GPU-based algorithms have greatly accelerated many machine learning methods; however, GPU memory is typically smaller than main memory, limiting the size of training data. In this paper, we describe an out-of-core GPU gradient boosting algorithm implemented in the XGBoost library. We show that much larger datasets can fit on a given GPU, without degrading model accuracy or training time. To the best of our knowledge, this is the first out-of-core GPU implementation of gradient boosting. Similar approaches can be applied to other machine learning algorithms

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that are computable by a given network. We study real infinitely differentiable (smooth) hierarchical functions implemented by feedforward neural networks via composing simpler functions in two cases: 1) each constituent function of the composition has fewer inputs than the resulting function; 2) constituent functions are in the more specific yet prevalent form of a non-linear univariate function (e.g. tanh) applied to a linear multivariate function. We establish that in each of these regimes there exist non-trivial algebraic partial differential equations (PDEs), which are satisfied by the computed functions. These PDEs are purely in terms of the partial derivatives and are dependent only on the topology of the network. For compositions of polynomial functions, the algebraic PDEs yield non-trivial equations (of degrees dependent only on the architecture) in the ambient polynomial space that are satisfied on the associated functional varieties. Conversely, we conjecture that such PDE constraints, once accompanied by appropriate non-singularity conditions and perhaps certain inequalities involving partial derivatives, guarantee that the smooth function under consideration can be represented by the network. The conjecture is verified in numerous examples including the case of tree architectures which are of neuroscientific interest. Our approach is a step toward formulating an algebraic description of functional spaces associated with specific neural networks, and may provide new, useful tools for constructing neural networks.

We propose a framework called HyperVAE for encoding distributions of distributions. When a target distribution is modeled by a VAE, its neural network parameters \theta is drawn from a distribution p(\theta) which is modeled by a hyper-level VAE. We propose a variational inference using Gaussian mixture models to implicitly encode the parameters \theta into a low dimensional Gaussian distribution. Given a target distribution, we predict the posterior distribution of the latent code, then use a matrix-network decoder to generate a posterior distribution q(\theta). HyperVAE can encode the parameters \theta in full in contrast to common hyper-networks practices, which generate only the scale and bias vectors as target-network parameters. Thus HyperVAE preserves much more information about the model for each task in the latent space. We discuss HyperVAE using the minimum description length (MDL) principle and show that it helps HyperVAE to generalize. We evaluate HyperVAE in density estimation tasks, outlier detection and discovery of novel design classes, demonstrating its efficacy.

In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to optimize the primal and dual variables iteratively. In each optimization iteration, we employ a proximal operator to search optimal solution in the primal space. We prove convergence of the proposed algorithm and show its non-asymptotic convergence rate. By utilizing the proposed primal-dual optimization technique, we propose a novel metric learning algorithm which learns an optimal feature transformation matrix in the Riemannian space of positive definite matrices. Preliminary experimental results on an optimal fund selection problem in fund of funds (FOF) management for quantitative investment showed its efficacy.

Machine learning shows remarkable success for recognizing patterns in data. Here we apply the machine learning (ML) for the diagnosis of early stage diabetes, which is known as a challenging task in medicine. Blood glucose levels are tightly regulated by two counter-regulatory hormones, insulin and glucagon, and the failure of the glucose homeostasis leads to the common metabolic disease, diabetes mellitus. It is a chronic disease that has a long latent period the complicates detection of the disease at an early stage. The vast majority of diabetics result from that diminished effectiveness of insulin action. The insulin resistance must modify the temporal profile of blood glucose. Thus we propose to use ML to detect the subtle change in the temporal pattern of glucose concentration. Time series data of blood glucose with sufficient resolution is currently unavailable, so we confirm the proposal using synthetic data of glucose profiles produced by a biophysical model that considers the glucose regulation and hormone action. Multi-layered perceptrons, convolutional neural networks, and recurrent neural networks all identified the degree of insulin resistance with high accuracy above $85\%$.

This work performs a non-asymptotic analysis of the general ized Lasso under the assumption of sub-exponential data. Our main results continue recent researc h on the benchmark case of (sub-)Gaussian sample distributions and thereby explore what conclusions are sti ll valid when going beyond. While many statistical features of the generalized Lasso remain unaffected (e.g., consistency), the key difference becomes manifested in the way how the complexity of the hypothesis set is measured. It t urns out that the estimation error can be controlled by means of two complexity parameters that arise naturally fro m a generic-chaining-based proof strategy . The output model can be non-realizable, while the only requirement for the input vector is a generic concentration inequality of Bernstein-type, which can be implemented for a variety of sub-exponential distributions. This abstract approach allows us to reproduce, unify, and extend previously known g uarantees for the generalized Lasso. In particular, we present applications to semi-parametric output models a nd phase retrieval via the lifted Lasso. Moreover, our findings are discussed in the context of sparse recovery and h igh-dimensional estimation problems.

In this paper we demonstrate methods for reliable and efficient training of discrete representation using Vector-Quantized Variational Auto-Encoder models (VQ-VAEs). Discrete latent variable models have been shown to learn nontrivial representations of speech, applicable to unsupervised voice conversion and reaching state-of-the-art performance on unit discovery tasks. For unsupervised representation learning, they became viable alternatives to continuous latent variable models such as the Variational Auto-Encoder (VAE). However, training deep discrete variable models is challenging, due to the inherent non-differentiability of the discretization operation. In this paper we focus on VQ-VAE, a state-of-the-art discrete bottleneck model shown to perform on par with its continuous counterparts. It quantizes encoder outputs with on-line $k$-means clustering. We show that the codebook learning can suffer from poor initialization and non-stationarity of clustered encoder outputs. We demonstrate that these can be successfully overcome by increasing the learning rate for the codebook and periodic date-dependent codeword re-initialization. As a result, we achieve more robust training across different tasks, and significantly increase the usage of latent codewords even for large codebooks. This has practical benefit, for instance, in unsupervised representation learning, where large codebooks may lead to disentanglement of latent representations.

Previous researches of sketches often considered sketches in pixel format and leveraged CNN based models in the sketch understanding. Fundamentally, a sketch is stored as a sequence of data points, a vector format representation, rather than the photo-realistic image of pixels. SketchRNN studied a generative neural representation for sketches of vector format by Long Short Term Memory networks (LSTM). Unfortunately, the representation learned by SketchRNN is primarily for the generation tasks, rather than the other tasks of recognition and retrieval of sketches. To this end and inspired by the recent BERT model, we present a model of learning Sketch Bidirectional Encoder Representation from Transformer (Sketch-BERT). We generalize BERT to sketch domain, with the novel proposed components and pre-training algorithms, including the newly designed sketch embedding networks, and the self-supervised learning of sketch gestalt. Particularly, towards the pre-training task, we present a novel Sketch Gestalt Model (SGM) to help train the Sketch-BERT. Experimentally, we show that the learned representation of Sketch-BERT can help and improve the performance of the downstream tasks of sketch recognition, sketch retrieval, and sketch gestalt.

We consider a setting where we have a set of data samples that were not uniformly sampled from a population, or where they were sampled from a different population than the one from which we wish to draw some conclusions. A common approach is to assign weights to the samples, so the resulting weighted distribution is representative of the population we wish to study. Here representative means that with the weights, certain expected values or probabilities match or are close to known values for the population we wish to study. A a very simple example, consider a data set where each sample is associated with a person. Our data set is 70% female, whereas we'd like to draw conclusions about a population that is 50% female. A simple solution is to down-weight the female samples, and up-weight the male samples in our data set, so the weighted fraction of females is 50%. As a more sophisticated example, suppose we have multiple groups, for example various combinations of sex, age group, income level, and education, and our goal is to find weights for our samples so the fractions of all these groups matches or approximates known fractions in the population we wish to study. In this case, there will be many possible assignments of weights that match the given fractions, and we need to choose a reasonable one. One approach is to maximize the entropy of the weights, subject to matching the given fractions.

In this paper, We propose a general Riemannian proximal optimization algorithm with guaranteed convergence to solve Markov decision process (MDP) problems. To model policy functions in MDP, we employ Gaussian mixture model (GMM) and formulate it as a nonconvex optimization problem in the Riemannian space of positive semidefinite matrices. For two given policy functions, we also provide its lower bound on policy improvement by using bounds derived from the Wasserstein distance of GMMs. Preliminary experiments show the efficacy of our proposed Riemannian proximal policy optimization algorithm.