Likelihood Gradient Research Articles

Random-Effects Substitution Models for Phylogenetics via Scalable Gradient Approximations.

Phylogenetic and discrete-trait evolutionary inference depend heavily on an appropriate characterization of the underlying character substitution process. In this paper, we present random-effects substitution models that extend common continuous-time Markov chain models into a richer class of processes capable of capturing a wider variety of substitution dynamics. As these random-effects substitution models often require many more parameters than their usual counterparts, inference can be both statistically and computationally challenging. Thus, we also propose an efficient approach to compute an approximation to the gradient of the data likelihood with respect to all unknown substitution model parameters. We demonstrate that this approximate gradient enables scaling of sampling-based inference, namely Bayesian inference via Hamiltonian Monte Carlo, under random-effects substitution models across large trees and state-spaces. Applied to a dataset of 583 SARS-CoV-2 sequences, an HKY model with random-effects shows strong signals of nonreversibility in the substitution process, and posterior predictive model checks clearly show that it is a more adequate model than a reversible model. When analyzing the pattern of phylogeographic spread of 1441 influenza A virus (H3N2) sequences between 14 regions, a random-effects phylogeographic substitution model infers that air travel volume adequately predicts almost all dispersal rates. A random-effects state-dependent substitution model reveals no evidence for an effect of arboreality on the swimming mode in the tree frog subfamily Hylinae. Simulations reveal that random-effects substitution models can accommodate both negligible and radical departures from the underlying base substitution model. We show that our gradient-based inference approach is over an order of magnitude more time efficient than conventional approaches.

Single‐Image SVBRDF Estimation with Learned Gradient Descent

AbstractRecovering spatially‐varying materials from a single photograph of a surface is inherently ill‐posed, making the direct application of a gradient descent on the reflectance parameters prone to poor minima. Recent methods leverage deep learning either by directly regressing reflectance parameters using feed‐forward neural networks or by learning a latent space of SVBRDFs using encoder‐decoder or generative adversarial networks followed by a gradient‐based optimization in latent space. The former is fast but does not account for the likelihood of the prediction, i.e., how well the resulting reflectance explains the input image. The latter provides a strong prior on the space of spatially‐varying materials, but this prior can hinder the reconstruction of images that are too different from the training data. Our method combines the strengths of both approaches. We optimize reflectance parameters to best reconstruct the input image using a recurrent neural network, which iteratively predicts how to update the reflectance parameters given the gradient of the reconstruction likelihood. By combining a learned prior with a likelihood measure, our approach provides a maximum a posteriori estimate of the SVBRDF. Our evaluation shows that this learned gradient‐descent method achieves state‐of‐the‐art performance for SVBRDF estimation on synthetic and real images.

Decomposition‐based maximum likelihood gradient iterative algorithm for multivariate systems with colored noise

SummaryIn this paper, we use the maximum likelihood principle and the negative gradient search principle to study the identification issues of the multivariate equation‐error systems whose outputs are contaminated by an moving average noise process. The model decomposition technique is used to decompose the system into several regressive identification subsystems based on the number of the outputs. In order to improve the parameter estimation accuracy, a decomposition‐based multivariate maximum likelihood gradient iterative algorithm is proposed by means of the maximum likelihood principle and the iterative identification method. The numerical simulation example indicates that the proposed method has better parameter estimation results than the compared decomposition‐based multivariate maximum likelihood gradient algorithm.

GWDALI: A Fisher-matrix based software for gravitational wave parameter-estimation beyond Gaussian approximation

We introduce GWDALI, a new Fisher-matrix, python based software that computes likelihood gradients to forecast parameter-estimation precision of arbitrary network of terrestrial gravitational wave detectors observing compact binary coalescences. The main new feature with respect to analogous software is to assess parameter uncertainties beyond Fisher-matrix approximation, using the derivative approximation for Likelihood (DALI). The software makes optional use of the LSC algorithm library LAL and the stochastic sampling algorithm Bilby, which can be used to perform Monte-Carlo sampling of exact or approximate likelihood functions. As an example we show comparison of estimated precision measurement of selected astrophysical parameters for both the actual likelihood, and for a variety of its derivative approximations, which turn out particularly useful when the Fisher matrix is not invertible.

Noise cleaning the precision matrix of short time series.

We present a comparison between various algorithms of inference of covariance and precision matrices in small data sets of real vectors of the typical length and dimension of human brain activity time series retrieved by functional magnetic resonance imaging (fMRI). Assuming a Gaussian model underlying the neural activity, the problem consists of denoising the empirically observed matrices to obtain a better estimator of the (unknown) true precision and covariance matrices. We consider several standard noise-cleaning algorithms and compare them on two types of data sets. The first type consists of synthetic time series sampled from a generative Gaussian model of which we can vary the fraction of dimensions per sample q and the strength of off-diagonal correlations. The second type consists of time series of fMRI brain activity of human subjects at rest. The reliability of each algorithm is assessed in terms of test-set likelihood and, in the case of synthetic data, of the distance from the true precision matrix. We observe that the so-called optimal rotationally invariant estimator, based on random matrix theory, leads to a significantly lower distance from the true precision matrix in synthetic data and higher test likelihood in natural fMRI data. We propose a variant of the optimal rotationally invariant estimator in which one of its parameters is optimzed by cross-validation. In the severe undersampling regime (large q) typical of fMRI series, it outperforms all the other estimators. We furthermore propose a simple algorithm based on an iterative likelihood gradient ascent, leading to very accurate estimations in weakly correlated synthetic data sets.

From Beginning to BEGANing: Role of Adversarial Learning in Reshaping Generative Models

Deep generative models, such as deep Boltzmann machines, focused on models that provided parametric specification of probability distribution functions. Such models are trained by maximizing intractable likelihood functions, and therefore require numerous approximations to the likelihood gradient. This underlying difficulty led to the development of generative machines such as generative stochastic networks, which do not represent the likelihood functions explicitly, like the earlier models, but are trained with exact backpropagation rather than the numerous approximations. These models use piecewise linear units that are having well behaved gradients. Generative machines were further extended with the introduction of an associative adversarial network leading to the generative adversarial nets (GANs) model by Goodfellow in 2014. The estimations in GANs process two multilayer perceptrons, called the generative model and the discriminative model. These are learned jointly by alternating the training of the two models, using game theory principles. However, GAN has many difficulties, including: the difficulty of training the models; criticality in the selection of hyper-parameters; difficulty in the control of generated samples; balancing the convergence of the discriminator and generator; and the problem of modal collapse. Since its inception, efforts have been made to tackle these issues one at a time or in multiples at several stages by many researchers. However, most of these have been handled efficiently in the boundary equilibrium generative adversarial networks (BEGAN) model introduced by Berthelot et al. in 2017. In this work we presented the advent of adversarial networks, starting with the history behind the models and c developments done on GANs until the BEGAN model was introduced. Since some time has elapsed since the proposal of BEGAN, we provided an up-to-date study, as well as future directions for various aspects of adversarial learning.

Maximum Likelihood Estimation of Destination Choice Models with Constrained Attractions

Attraction constraints are common and often appropriate for destination choice models, including, but not limited to, doubly constrained gravity distribution models. Estimation of their parameters by discrete-choice methods, however, seldom accounts for the constraints, despite bias known from their omission. For multinomial logit destination choice, this paper first formulates the parameter estimation for maximum likelihood of a set of observations, subject to exogenous attraction constraints on the model’s application to a population. Second, this formulation is extended for attraction constraints being linear combinations of size variables with coefficients to be estimated. Both the utility and size parameter estimations are distinct from the well-known formulation for unconstrained estimation, because of the contribution of the constraining shadow-price utilities to the likelihood gradients. Gradients and the Hessian are identified, along with adaptations of them for Newton-Raphson parameter updates and Cramér-Rao bounds. Experiments demonstrate its computational tractability and performance, and compare its estimations with those of unconstrained and other methods.

An unsupervised defect detection model for a dry carbon fiber textile

Inspection of dry carbon textiles is a key step to ensure quality in aerospace manufacturing. Due to the rarity and variety of defects, collecting a comprehensive defect dataset is difficult, while collecting ‘normal’ data is comparatively easy. In this paper, we present an unsupervised defect detection method for carbon fiber textiles that meets four key criteria for industrial applicability: using only ‘normal’ data, achieving high accuracy even on small and subtle defects, allowing visual interpretation, and achieving real-time performance. We combine a Visual Transformer Encoder and a Normalizing Flow to gather global context from input images and directly produce an image likelihood which is then used as an anomaly score. We demonstrate that when trained on only 150 normal samples, our method correctly detects 100% of anomalies with a 0% false positive rate on a industrial carbon fabric dataset with 34 real defect samples, including subtle stray fiber defects covering only 1% image area where previous methods are shown to fail. We validate the performance on the large public defect dataset MVTec-AD Textures, where we outperform previous work by 4–10%, proving the applicability of our method to other domains. Additionally, we propose a method to extract interpretable anomaly maps from Visual Transformer Attention Rollout and Image Likelihood Gradients that produces convincing explanations for detected anomalies. Finally, we show that the inference time for the model is acceptable at 32 ms, achieving real-time performance.

Gain-loss-duplication models for copy number evolution on a phylogeny: Exact algorithms for computing the likelihood and its gradient

Gene gain-loss-duplication models are commonly based on continuous-time birth–death processes. Employed in a phylogenetic context, such models have been increasingly popular in studies of gene content evolution across multiple genomes. While the applications are becoming more varied and demanding, bioinformatics methods for probabilistic inference on copy numbers (or integer-valued evolutionary characters, in general) are scarce.We describe a flexible probabilistic framework for phylogenetic gain-loss-duplication models. The framework is based on a novel elementary representation by dependent random variables with well-characterized conditional distributions: binomial, Pólya (negative binomial), and Poisson.The corresponding graphical model yields exact numerical procedures for computing the likelihood and the posterior distribution of ancestral copy numbers. The resulting algorithms take quadratic time in the total number of copies. In addition, we show how the likelihood gradient can be computed by a linear-time algorithm.

Knowledge-Based Unfolded State Model for Protein Design.

The design of proteins and miniproteins is an important challenge. Designed variants should be stable, meaning the folded/unfolded free energy difference should be large enough. Thus, the unfolded state plays a central role. An extended peptide model is often used, where side chains interact with solvent and nearby backbone, but not each other. The unfolded energy is then a function of sequence composition only and can be empirically parametrized. If the space of sequences is explored with a Monte Carlo procedure, protein variants will be sampled according to a well-defined Boltzmann probability distribution. We can then choose unfolded model parameters to maximize the probability of sampling native-like sequences. This leads to a well-defined maximum likelihood framework. We present an iterative algorithm that follows the likelihood gradient. The method is presented in the context of our Proteus software, as a detailed downloadable tutorial. The unfolded model is combined with a folded model that uses molecular mechanics and a Generalized Born solvent. It was optimized for three PDZ domains and then used to redesign them. The sequences sampled are native-like and similar to a recent PDZ design study that was experimentally validated.

MLE-Guided Parameter Search for Task Loss Minimization in Neural Sequence Modeling

Neural autoregressive sequence models are used to generate sequences in a variety of natural language processing (NLP) tasks, where they are evaluated according to sequence-level task losses. These models are typically trained with maximum likelihood estimation, which ignores the task loss, yet empirically performs well as a surrogate objective. Typical approaches to directly optimizing the task loss such as policy gradient and minimum risk training are based around sampling in the sequence space to obtain candidate update directions that are scored based on the loss of a single sequence. In this paper, we develop an alternative method based on random search in the parameter space that leverages access to the maximum likelihood gradient. We propose maximum likelihood guided parameter search (MGS), which samples from a distribution over update directions that is a mixture of random search around the current parameters and around the maximum likelihood gradient, with each direction weighted by its improvement in the task loss. MGS shifts sampling to the parameter space, and scores candidates using losses that are pooled from multiple sequences. Our experiments show that MGS is capable of optimizing sequence-level losses, with substantial reductions in repetition and non-termination in sequence completion, and similar improvements to those of minimum risk training in machine translation.

Research and Analysis of Maximum Likelihood Parameter Identification Based on The Recursion of Longdongnan Economic Model

By establishing the regional economic model of southeast Gansu Economic Model as the maximum likelihood parameter identification,the maximum likelihood identification is an estimation method based on probability and statistics theory,by constructing the likelihood function with independent variables and maximizing the likelihood function,the model has good statistical properties and is widely used in many fields.However, the research of maximum likelihood identification method is still limited. Therefore, it is of theoretical significance and academic value to study the maximum likelihood identification method for linear systems and Hammerstein nonlinear systems by combining data filtering technique, hierarchical identification principle and multi-innovation identification theory. In order to improve the identification accuracy, maximum likelihood gradient iteration and maximum likelihood gradient iteration based on finite data window are proposed for output error moving average system.This paper holds that the pattern conforms to the requirements of economic development of Southeast Longnan and has a strong reference for other regions.The simulation results verify the feasibility and validity of the identification modeling method.

Gaussian process optimization with failures: classification and convergence proof

We consider the optimization of a computer model where each simulation either fails or returns a valid output performance. We first propose a new joint Gaussian process model for classification of the inputs (computation failure or success) and for regression of the performance function. We provide results that allow for a computationally efficient maximum likelihood estimation of the covariance parameters, with a stochastic approximation of the likelihood gradient. We then extend the classical improvement criterion to our setting of joint classification and regression. We provide an efficient computation procedure for the extended criterion and its gradient. We prove the almost sure convergence of the global optimization algorithm following from this extended criterion. We also study the practical performances of this algorithm, both on simulated data and on a real computer model in the context of automotive fan design.

A pattern analysis based underwater video segmentation system for target object detection

Detecting and classifying the target objects in the underwater videos is the primary and essential operation in this modern era. The present works proposed the pattern extraction, segmentation and classification techniques for target object detection in underwater images. These techniques were found to be lacking with the following limitations, such as inefficient computation, inaccurate results, and increased cost-efficiency. Thus, this work targets to introduce a new pattern extraction based classification system for processing underwater images. As the first and foremost thing, the input underwater picture is preprocessed for eliminating the noise by applying the Laplacian Bellman filtering technique. After that, the histogram equalization is utilized to enhance the quality of the source picture. Once the image is noise-free, the patterns are extracted from it with the help of the likelihood gradient pattern technique. Subsequently, the label formation and blob extraction processes are performed in an orderly manner to track the target object accurately. In this work, the novelty is seen implemented in both the preprocessing and the feature analysis stages by developing a novel technique. The significant advantages of this work are: yielding the improved image quality, by being the efficient texture pattern extractor, and they also do not require any additional information and adjustments. While under simulation, the fulfilment attained in the proposed techniques and the appropriate literature methodologies are evaluated and validated with the performance measures like accuracy, sensitivity, specificity, average time, precision, F1-measure, and the filtering features like entropy, contrast, and the correlation.

On hypothesis testing inference in location-scale models under model misspecification

The likelihood ratio, Wald, score and gradient test statistics can result in misleading conclusions when the assumed parametric model to the data at hand is not correctly specified. To overcome this issue, robust versions of these test statistics have been proposed in the statistic literature under model misspecification. In this paper, we address the issue of performing hypothesis testing inference in location-scale models under model misspecification. Monte Carlo simulation experiments are carried out to verify the performance of the robust test statistics, as well as usual test statistics (i.e. non-robust), in the class of location-scale models under model misspecification. The simulation results reveal that the robust tests we propose are more reliable than the usual tests since they lead to an accurate inference. An empirical application to real data is considered for illustrative purposes.

Data filtering based maximum likelihood gradient estimation algorithms for a multivariate equation-error system with ARMA noise

In this paper, we use the maximum likelihood principle and the data filtering technique to study the identification issue of the multivariate equation-error system whose outputs are contaminated by an ARMA noise process. The key is to break the system into several regressive identification subsystems based on the number of the outputs. Then a multivariate equation-error subsystem is transformed into a filtered model and a filtered noise model, and a filtering based maximum likelihood extended stochastic gradient algorithm is derived to estimate the parameters of these two models. The filtering based maximum likelihood extended stochastic gradient algorithm has higher parameter estimation accuracy than the maximum likelihood generalized extended stochastic gradient algorithm and the maximum likelihood recursive generalized extended least squares algorithm. The simulation examples indicate that the proposed methods work well.

Using a Coproduction Approach to Map Future Forest Retention Likelihood in the Southeastern United States

AbstractForestlands in the Southern United States provide important ecological and socioeconomic services that are under increasing pressure from development and other stressors. We used a coproduction approach with 50+ stakeholders to create a qualitative, spatially explicit Forest Retention Index to provide a gradient of future forest retention likelihood on presently forested lands. An estimated 17.7 million acres are at high risk of forest loss by 2060. These losses are largely driven by urbanization, but sea-level rise plays a key role in some coastal areas. Approximately 59 percent of southern forest is projected to be retained with High or Very High likelihood but is unevenly distributed among southern states. Approximately 8 percent of highly biodiverse forest is at high risk of land-use conversion. This tool provides a collaborative, transparent, and defensible mapping product that can aid in identification of key areas where retaining forest is critical to maintaining ecological and socioeconomic integrity.

Block Belief Propagation for Parameter Learning in Markov Random Fields

Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models. In this paper, we propose block belief propagation learning (BBPL), which uses block-coordinate updates of approximate marginals to compute approximate gradients, removing the need to compute inference on the entire graphical model. Thus, the iteration complexity of BBPL does not scale with the size of the graphs. We prove that the method converges to the same solution as that obtained by using full inference per iteration, despite these approximations, and we empirically demonstrate its scalability improvements over standard training methods.

Optimizing restricted Boltzmann machine learning by injecting Gaussian noise to likelihood gradient approximation

Restricted Boltzmann machines (RBMs) can be trained by applying stochastic gradient ascent to the objective function as the maximum likelihood learning. However, it is a difficult task due to the intractability of marginalization function gradient. Several methodologies have been proposed by adopting Gibbs Markov chain to approximate this intractability including Contrastive Divergence, Persistent Contrastive Divergence, and Fast Contrastive Divergence. In this paper, we propose an optimization which is injecting noise to underlying Monte Carlo estimation. We introduce two novel learning algorithms. They are Noisy Persistent Contrastive Divergence (NPCD), and further Fast Noisy Persistent Contrastive Divergence (FNPCD). We prove that the NPCD and FNPCD algorithms benefit on the average to equilibrium state with satisfactory condition. We have performed empirical investigation of diverse CD-based approaches and found that our proposed methods frequently obtain higher classification performance than traditional approaches on several benchmark tasks in standard image classification tasks such as MNIST, basic, and rotation datasets.

Multi-centroid diastolic duration distribution based HSMM for heart sound segmentation

Abstract This paper presents a multi-centroid diastolic duration model for the hidden semi-Markov model (HSMM) based heart sound segmentation. The centroids are calculated by hierarchical agglomerative clustering of the neighboring diastolic duration values using Ward's method until center of clusters are found at least a systolic duration apart. The multiple peak distribution yields a sharper gradient of likelihood around the expected centroids and improves the discriminability of similar observations. The peak density at each centroid acts as a reference point for the HSMM to determine the origin of the hidden-state and adjust the corresponding state duration based on the maximum likelihood criterion. This model overcomes the limitation of the single peak mean value model that may overfit the duration distribution when the heart rate variation is relatively large. An extended logistic regression-HSMM algorithm using the proposed duration model is presented for the heart sound segmentation. In addition, the total variation filter is used to attenuate the effect of noises and emphasize the fundamental heart sounds, S1 and S2. The proposed method is evaluated on the training-set-a of 2016 Physionet/Computing in Cardiology Challenge and yields an average F1 score of 98.36 ± 0.43.