arXiv subjects

Masoud Asgharian

Publications and source records attributed to Masoud Asgharian.

34 records · Page 2Linked to original sources

arXiv2023

Mathematical Challenges in Deep Learning

Deep models are dominating the artificial intelligence (AI) industry since the ImageNet challenge in 2012. The size of deep models is increasing ever since, which brings new challenges to this field with applications in cell phones, personal computers, autonomous cars, and wireless base stations. Here we list a set of problems, ranging from training, inference, generalization bound, and optimization with some formalism to communicate these challenges with mathematicians, statisticians, and theoretical computer scientists. This is a subjective view of the research questions in deep learning that benefits the tech industry in long run.

cs.LG↗

arXiv2023

Towards Fine-tuning Pre-trained Language Models with Integer Forward and Backward Propagation

The large number of parameters of some prominent language models, such as BERT, makes their fine-tuning on downstream tasks computationally intensive and energy hungry. Previously researchers were focused on lower bit-width integer data types for the forward propagation of language models to save memory and computation. As for the backward propagation, however, only 16-bit floating-point data type has been used for the fine-tuning of BERT. In this work, we use integer arithmetic for both forward and back propagation in the fine-tuning of BERT. We study the effects of varying the integer bit-width on the model's metric performance. Our integer fine-tuning uses integer arithmetic to perform forward propagation and gradient computation of linear, layer-norm, and embedding layers of BERT. We fine-tune BERT using our integer training method on SQuAD v1.1 and SQuAD v2., and GLUE benchmark. We demonstrate that metric performance of fine-tuning 16-bit integer BERT matches both 16-bit and 32-bit floating-point baselines. Furthermore, using the faster and more memory efficient 8-bit integer data type, integer fine-tuning of BERT loses an average of 3.1 points compared to the FP32 baseline.

cs.LG↗

arXiv2023

On the Convergence of Stochastic Gradient Descent in Low-precision Number Formats

Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually performed in single-precision floating-point number format. The convergence of single-precision SGD is normally aligned with the theoretical results of real numbers since they exhibit negligible error. However, the numerical error increases when the computations are performed in low-precision number formats. This provides compelling reasons to study the SGD convergence adapted for low-precision computations. We present both deterministic and stochastic analysis of the SGD algorithm, obtaining bounds that show the effect of number format. Such bounds can provide guidelines as to how SGD convergence is affected when constraints render the possibility of performing high-precision computations remote.

cs.LG↗

arXiv2023

Is Integer Arithmetic Enough for Deep Learning Training?

The ever-increasing computational complexity of deep learning models makes their training and deployment difficult on various cloud and edge platforms. Replacing floating-point arithmetic with low-bit integer arithmetic is a promising approach to save energy, memory footprint, and latency of deep learning models. As such, quantization has attracted the attention of researchers in recent years. However, using integer numbers to form a fully functional integer training pipeline including forward pass, back-propagation, and stochastic gradient descent is not studied in detail. Our empirical and mathematical results reveal that integer arithmetic seems to be enough to train deep learning models. Unlike recent proposals, instead of quantization, we directly switch the number representation of computations. Our novel training method forms a fully integer training pipeline that does not change the trajectory of the loss and accuracy compared to floating-point, nor does it need any special hyper-parameter tuning, distribution adjustment, or gradient clipping. Our experimental results show that our proposed method is effective in a wide variety of tasks such as classification (including vision transformers), object detection, and semantic segmentation.

cs.LG↗

arXiv2022

Training Integer-Only Deep Recurrent Neural Networks

Recurrent neural networks (RNN) are the backbone of many text and speech applications. These architectures are typically made up of several computationally complex components such as; non-linear activation functions, normalization, bi-directional dependence and attention. In order to maintain good accuracy, these components are frequently run using full-precision floating-point computation, making them slow, inefficient and difficult to deploy on edge devices. In addition, the complex nature of these operations makes them challenging to quantize using standard quantization methods without a significant performance drop. We present a quantization-aware training method for obtaining a highly accurate integer-only recurrent neural network (iRNN). Our approach supports layer normalization, attention, and an adaptive piecewise linear (PWL) approximation of activation functions, to serve a wide range of state-of-the-art RNNs. The proposed method enables RNN-based language models to run on edge devices with $2\times$ improvement in runtime, and $4\times$ reduction in model size while maintaining similar accuracy as its full-precision counterpart.

cs.LG↗

arXiv2022

EuclidNets: An Alternative Operation for Efficient Inference of Deep Learning Models

With the advent of deep learning application on edge devices, researchers actively try to optimize their deployments on low-power and restricted memory devices. There are established compression method such as quantization, pruning, and architecture search that leverage commodity hardware. Apart from conventional compression algorithms, one may redesign the operations of deep learning models that lead to more efficient implementation. To this end, we propose EuclidNet, a compression method, designed to be implemented on hardware which replaces multiplication, $xw$, with Euclidean distance $(x-w)^2$. We show that EuclidNet is aligned with matrix multiplication and it can be used as a measure of similarity in case of convolutional layers. Furthermore, we show that under various transformations and noise scenarios, EuclidNet exhibits the same performance compared to the deep learning models designed with multiplication operations.

cs.LG↗

arXiv2022

Accelerated Gradient Methods for Sparse Statistical Learning with Nonconvex Penalties

Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov's AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery.

math.OC↗

arXiv2021

A Causal Direction Test for Heterogeneous Populations

A probabilistic expert system emulates the decision-making ability of a human expert through a directional graphical model. The first step in building such systems is to understand data generation mechanism. To this end, one may try to decompose a multivariate distribution into product of several conditionals, and evolving a blackbox machine learning predictive models towards transparent cause-and-effect discovery. Most causal models assume a single homogeneous population, an assumption that may fail to hold in many applications. We show that when the homogeneity assumption is violated, causal models developed based on such assumption can fail to identify the correct causal direction. We propose an adjustment to a commonly used causal direction test statistic by using a $k$-means type clustering algorithm where both the labels and the number of components are estimated from the collected data to adjust the test statistic. Our simulation result show that the proposed adjustment significantly improves the performance of the causal direction test statistic for heterogeneous data. We study large sample behaviour of our proposed test statistic and demonstrate the application of the proposed method using real data.

stat.ME↗

arXiv2019

A Convergence Diagnostic for Bayesian Clustering

In many applications of Bayesian clustering, posterior sampling on the discrete state space of cluster allocations is achieved via Markov chain Monte Carlo (MCMC) techniques. As it is typically challenging to design transition kernels to explore this state space efficiently, MCMC convergence diagnostics for clustering applications is especially important. For general MCMC problems, state-of-the-art convergence diagnostics involve comparisons across multiple chains. However, single-chain alternatives can be appealing for computationally intensive and slowly-mixing MCMC, as is typically the case for Bayesian clustering. Thus, we propose here a single-chain convergence diagnostic specifically tailored to discrete-space MCMC. Namely, we consider a Hotelling-type statistic on the highest probability states, and use regenerative sampling theory to derive its equilibrium distribution. By leveraging information from the unnormalized posterior, our diagnostic protects against seemingly convergent chains in which the relative frequency of visited states is incorrect. The methodology is illustrated with a Bayesian clustering analysis of genetic mutants of the flowering plant Arabidopsis thaliana.

stat.CO↗

arXiv2015

Variable Selection in Causal Inference using a Simultaneous Penalization Method

In the causal adjustment setting, variable selection techniques based on one of either the outcome or treatment allocation model can result in the omission of confounders, which leads to bias, or the inclusion of spurious variables, which leads to variance inflation, in the propensity score. We propose a variable selection method based on a penalized objective function which considers the outcome and treatment assignment models simultaneously. The proposed method facilitates confounder selection in high-dimensional settings. We show that under regularity conditions our method attains the oracle property. The selected variables are used to form a doubly robust regression estimator of the treatment effect. We show that under some conditions our method attains the oracle property. Simulation results are presented and economic growth data are analyzed. Specifically, we study the effect of life expectancy as a measure of population health on the average growth rate of gross domestic product per capita.

stat.ME↗

arXiv2014

Variable Selection in Causal Inference Using Penalization

In the causal adjustment setting, variable selection techniques based on either the outcome or treatment allocation model can result in the omission of confounders or the inclusion of spurious variables in the propensity score. We propose a variable selection method based on a penalized likelihood which considers the response and treatment assignment models simultaneously. The proposed method facilitates confounder selection in high-dimensional settings. We show that under some conditions our method attains the oracle property. The selected variables are used to form a double robust regression estimator of the treatment effect. Simulation results are presented and economic growth data are analyzed.

math.ST↗

arXiv2013

The Propensity Score Estimation in the Presence of Length-biased Sampling: A Nonparametric Adjustment Approach

The pervasive use of prevalent cohort studies on disease duration, increasingly calls for appropriate methodologies to account for the biases that invariably accompany samples formed by such data. It is well-known, for example, that subjects with shorter lifetime are less likely to be present in such studies. Moreover, certain covariate values could be preferentially selected into the sample, being linked to the long-term survivors. The existing methodology for estimation of the propensity score using data collected on prevalent cases requires the correct conditional survival/hazard function given the treatment and covariates. This requirement can be alleviated if the disease under study has stationary incidence, the so-called stationarity assumption. We propose a nonparametric adjustment technique based on a weighted estimating equation for estimating the propensity score which does not require modeling the conditional survival/hazard function when the stationarity assumption holds. Large sample properties of the estimator is established and its small sample behavior is studied via simulation.

math.ST↗

arXiv2012

Large-sample study of the kernel density estimators under multiplicative censoring

The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989) 751--761] is an incomplete data problem whereby two independent samples from the lifetime distribution $G$, $\mathcal{X}_m=(X_1,...,X_m)$ and $\mathcal{Z}_n=(Z_1,...,Z_n)$, are observed subject to a form of coarsening. Specifically, sample $\mathcal{X}_m$ is fully observed while $\mathcal{Y}_n=(Y_1,...,Y_n)$ is observed instead of $\mathcal{Z}_n$, where $Y_i=U_iZ_i$ and $(U_1,...,U_n)$ is an independent sample from the standard uniform distribution. Vardi [Biometrika 76 (1989) 751--761] showed that this model unifies several important statistical problems, such as the deconvolution of an exponential random variable, estimation under a decreasing density constraint and an estimation problem in renewal processes. In this paper, we establish the large-sample properties of kernel density estimators under the multiplicative censoring model. We first construct a strong approximation for the process $\sqrt{k}(\hat{G}-G)$, where $\hat{G}$ is a solution of the nonparametric score equation based on $(\mathcal{X}_m,\mathcal{Y}_n)$, and $k=m+n$ is the total sample size. Using this strong approximation and a result on the global modulus of continuity, we establish conditions for the strong uniform consistency of kernel density estimators. We also make use of this strong approximation to study the weak convergence and integrated squared error properties of these estimators. We conclude by extending our results to the setting of length-biased sampling.

math.ST↗

arXiv2008

On the incidence-prevalence relation and length-biased sampling

For many diseases, logistic and other constraints often render large incidence studies difficult, if not impossible, to carry out. This becomes a drawback, particularly when a new incidence study is needed each time the disease incidence rate is investigated in a different population. However, by carrying out a prevalent cohort study with follow-up it is possible to estimate the incidence rate if it is constant. In this paper we derive the maximum likelihood estimator (MLE) of the overall incidence rate, $λ$, as well as age-specific incidence rates, by exploiting the well known epidemiologic relationship, prevalence = incidence $\times$ mean duration ($P = λ\times μ$). We establish the asymptotic distributions of the MLEs, provide approximate confidence intervals for the parameters, and point out that the MLE of $λ$ is asymptotically most efficient. Moreover, the MLE of $λ$ is the natural estimator obtained by substituting the marginal maximum likelihood estimators for P and $μ$, respectively, in the expression $P = λ\times μ$. Our work is related to that of Keiding (1991, 2006), who, using a Markov process model, proposed estimators for the incidence rate from a prevalent cohort study \emph{without} follow-up, under three different scenarios. However, each scenario requires assumptions that are both disease specific and depend on the availability of epidemiologic data at the population level. With follow-up, we are able to remove these restrictions, and our results apply in a wide range of circumstances. We apply our methods to data collected as part of the Canadian Study of Health and Ageing to estimate the incidence rate of dementia amongst elderly Canadians.

stat.ME↗

arXiv2008

Principle of detailed balance and convergence assessment of Markov Chain Monte Carlo methods and simulated annealing

Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from it is available. Although a wealth of diagnostic tools for convergence assessment of MCMC methods have been proposed in the last two decades, the search for a dependable and easy to implement tool is ongoing. We present in this article a criterion based on the principle of detailed balance which provides a qualitative assessment of the convergence of a given chain. The criterion is based on the behaviour of a one-dimensional statistic, whose asymptotic distribution under the assumption of stationarity is derived; our results apply under weak conditions and have the advantage of being completely intuitive. We implement this criterion as a stopping rule for simulated annealing in the problem of finding maximum likelihood estimators for parameters of a 20-component mixture model. We also apply it to the problem of sampling from a 10-dimensional funnel distribution via slice sampling and the Metropolis-Hastings algorithm. Furthermore, based on this convergence criterion we define a measure of efficiency of one algorithm versus another.

stat.CO↗

arXiv2006

Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data

Right censored survival data collected on a cohort of prevalent cases with constant incidence are length-biased, and may be used to estimate the length-biased (i.e., prevalent-case) survival function. When the incidence rate is constant, so-called stationarity of the incidence, it is more efficient to use this structure for unconditional statistical inference than to carry out an analysis by conditioning on the observed truncation times. It is well known that, due to the informative censoring for prevalent cohort data, the Kaplan--Meier estimator is not the unconditional NPMLE of the length-biased survival function and the asymptotic properties of the NPMLE do not follow from any known result. We present here a detailed derivation of the asymptotic properties of the NPMLE of the length-biased survival function from right censored prevalent cohort survival data with follow-up. In particular, we show that the NPMLE is uniformly strongly consistent, converges weakly to a Gaussian process, and is asymptotically efficient. One important spin-off from these results is that they yield the asymptotic properties of the NPMLE of the incident-case survival function [see Asgharian, M'Lan and Wolfson J. Amer. Statist. Assoc. 97 (2002) 201--209], which is often of prime interest in a prevalent cohort study. Our results generalize those given by Vardi and Zhang [Ann. Statist. 20 (1992) 1022--1039] under multiplicative censoring, which we show arises as a degenerate case in a prevalent cohort setting.

math.ST↗