As the amount of text data continues to grow, topic modeling is serving an important role in understanding the content hidden by the overwhelming quantity of documents. One popular topic modeling approach is non-negative matrix factorization (NMF), an unsupervised machine learning (ML) method. Recently, Semantic NMF with automatic model selection (SeNMFk) has been proposed as a modification to NMF. In addition to heuristically estimating the number of topics, SeNMFk also incorporates the semantic structure of the text. This is performed by jointly factorizing the term frequency-inverse document frequency (TF-IDF) matrix with the co-occurrence/word-context matrix, the values of which represent the number of times two words co-occur in a predetermined window of the text. In this paper, we introduce a novel distributed method, SeNMFk-SPLIT, for semantic topic extraction suitable for large corpora. Contrary to SeNMFk, our method enables the joint factorization of large documents by decomposing the word-context and term-document matrices separately. We demonstrate the capability of SeNMFk-SPLIT by applying it to the entire artificial intelligence (AI) and ML scientific literature uploaded on arXiv.
In this paper, we consider the meta learning problem for estimating the graphs associated with high-dimensional Ising models, using the method of $\ell_1$-regularized logistic regression for neighborhood selection of each node. Our goal is to use the information learned from the auxiliary tasks in the learning of the novel task to reduce its sufficient sample complexity. To this end, we propose a novel generative model as well as an improper estimation method. In our setting, all the tasks are \emph{similar} in their \emph{random} model parameters and supports. By pooling all the samples from the auxiliary tasks to \emph{improperly} estimate a single parameter vector, we can recover the true support union, assumed small in size, with a high probability with a sufficient sample complexity of $\Omega(1) $ per task, for $K = \Omega(d^3 \log p ) $ tasks of Ising models with $p$ nodes and a maximum neighborhood size $d$. Then, with the support for the novel task restricted to the estimated support union, we prove that consistent neighborhood selection for the novel task can be obtained with a reduced sufficient sample complexity of $\Omega(d^3 \log d)$.
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed processing and storage solutions. We propose a two-stage distributed and robust statistical inference procedures coping with high-dimensional models by promoting sparsity. In the first stage, known as model selection, relevant predictors are locally selected by applying robust Lasso estimators to the distinct subsets of data. The variable selections from each computation node are then fused by a voting scheme to find the sparse basis for the complete data set. It identifies the relevant variables in a robust manner. In the second stage, the developed statistically robust and computationally efficient bootstrap methods are employed. The actual inference constructs confidence intervals, finds parameter estimates and quantifies standard deviation. Similar to stage 1, the results of local inference are communicated to the fusion center and combined there. By using analytical methods, we establish the favorable statistical properties of the robust and computationally efficient bootstrap methods including consistency for a fixed number of predictors, and robustness. The proposed two-stage robust and distributed inference procedures demonstrate reliable performance and robustness in variable selection, finding confidence intervals and bootstrap approximations of standard deviations even when data is high-dimensional and contaminated by outliers.
We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with embedded spatiotemporal dynamics to model georeferenced data observed in a functional domain. Thus, the parameters of interest are functions across this domain. The algorithm simultaneously selects the relevant spline basis functions and regressors that are used to model the fixed-effects relationship between the response variable and the covariates. In this way, it automatically shrinks to zero irrelevant parts of the functional coefficients or the entire effect of irrelevant regressors. The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (LASSO) penalty function, wherein the weights are obtained by the unpenalised f-HDGM maximum-likelihood estimators. The computational burden of maximisation is drastically reduced by a local quadratic approximation of the likelihood. Through a Monte Carlo simulation study, we analysed the performance of the algorithm under different scenarios, including strong correlations among the regressors. We showed that the penalised estimator outperformed the unpenalised estimator in all the cases we considered. We applied the algorithm to a real case study in which the recording of the hourly nitrogen dioxide concentrations in the Lombardy region in Italy was modelled as a functional process with several weather and land cover covariates.
The authors propose new additive models for binary outcomes, where the components are copula-based regression models (Noh et al, 2013), and designed such that the model may capture potentially complex interaction effects. The models do not require discretisation of continuous covariates, and are therefore suitable for problems with many such covariates. A fitting algorithm, and efficient procedures for model selection and evaluation of the components are described. Software is provided in the R-package copulaboost. Simulations and illustrations on data sets indicate that the method's predictive performance is either better than or comparable to the other methods.
Data-driven science is an emerging paradigm where scientific discoveries depend on the execution of computational AI models against rich, discipline-specific datasets. With modern machine learning frameworks, anyone can develop and execute computational models that reveal concepts hidden in the data that could enable scientific applications. For important and widely used datasets, computing the performance of every computational model that can run against a dataset is cost prohibitive in terms of cloud resources. Benchmarking approaches used in practice use representative datasets to infer performance without actually executing models. While practicable, these approaches limit extensive dataset profiling to a few datasets and introduce bias that favors models suited for representative datasets. As a result, each dataset's unique characteristics are left unexplored and subpar models are selected based on inference from generalized datasets. This necessitates a new paradigm that introduces dataset profiling into the model selection process. To demonstrate the need for dataset-specific profiling, we answer two questions:(1) Can scientific datasets significantly permute the rank order of computational models compared to widely used representative datasets? (2) If so, could lightweight model execution improve benchmarking accuracy? Taken together, the answers to these questions lay the foundation for a new dataset-aware benchmarking paradigm.
Systems biology seeks to create math models of biological systems to reduce inherent biological complexity and provide predictions for applications such as therapeutic development. However, it remains a challenge to determine which math model is correct and how to arrive optimally at the answer. We present an algorithm for automated biological model selection using mathematical models of systems biology and likelihood free inference methods. Our algorithm shows improved performance in arriving at correct models without a priori information over conventional heuristics used in experimental biology and random search. This method shows promise to accelerate biological basic science and drug discovery.
The Gini index does not give a strictly consistent scoring rule in general. Therefore, maximizing the Gini index may lead to wrong decisions. The main issue is that the Gini index is a rank-based score that is not calibration-sensitive. We show that the Gini index allows for strictly consistent scoring if we restrict to the class of auto-calibrated regression models.
Graph Neural Networks (GNNs), inspired by Convolutional Neural Networks (CNNs), aggregate the message of nodes' neighbors and structure information to acquire expressive representations of nodes for node classification, graph classification, and link prediction. Previous studies have indicated that GNNs are vulnerable to Membership Inference Attacks (MIAs), which infer whether a node is in the training data of GNNs and leak the node's private information, like the patient's disease history. The implementation of previous MIAs takes advantage of the models' probability output, which is infeasible if GNNs only provide the prediction label (label-only) for the input. In this paper, we propose a label-only MIA against GNNs for node classification with the help of GNNs' flexible prediction mechanism, e.g., obtaining the prediction label of one node even when neighbors' information is unavailable. Our attacking method achieves around 60\% accuracy, precision, and Area Under the Curve (AUC) for most datasets and GNN models, some of which are competitive or even better than state-of-the-art probability-based MIAs implemented under our environment and settings. Additionally, we analyze the influence of the sampling method, model selection approach, and overfitting level on the attack performance of our label-only MIA. Both of those factors have an impact on the attack performance. Then, we consider scenarios where assumptions about the adversary's additional dataset (shadow dataset) and extra information about the target model are relaxed. Even in those scenarios, our label-only MIA achieves a better attack performance in most cases. Finally, we explore the effectiveness of possible defenses, including Dropout, Regularization, Normalization, and Jumping knowledge. None of those four defenses prevent our attack completely.
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the impact of input data uncertainty in the model outputs to increase robustness. However, most developments are applicable assuming that the input data adheres to a parametric family of distributions. We propose a unified output analysis framework for simulation and machine learning outputs through the lens of Monte Carlo sampling. This framework provides nonparametric quantification of the variance and bias induced in the outputs with higher-order accuracy. Our new bias-corrected estimation from the model outputs leverages the extension of fast iterative bootstrap sampling and higher-order influence functions. For the scalability of the proposed estimation methods, we devise budget-optimal rules and leverage control variates for variance reduction. Our theoretical and numerical results demonstrate a clear advantage in building more robust confidence intervals from the model outputs with higher coverage probability.
Transfer learning through the use of pre-trained models has become a growing trend for the machine learning community. Consequently, numerous pre-trained models are released online to facilitate further research. However, it raises extensive concerns on whether these pre-trained models would leak privacy-sensitive information of their training data. Thus, in this work, we aim to answer the following questions: "Can we effectively recover private information from these pre-trained models? What are the sufficient conditions to retrieve such sensitive information?" We first explore different statistical information which can discriminate the private training distribution from other distributions. Based on our observations, we propose a novel private data reconstruction framework, SecretGen, to effectively recover private information. Compared with previous methods which can recover private data with the ground true prediction of the targeted recovery instance, SecretGen does not require such prior knowledge, making it more practical. We conduct extensive experiments on different datasets under diverse scenarios to compare SecretGen with other baselines and provide a systematic benchmark to better understand the impact of different auxiliary information and optimization operations. We show that without prior knowledge about true class prediction, SecretGen is able to recover private data with similar performance compared with the ones that leverage such prior knowledge. If the prior knowledge is given, SecretGen will significantly outperform baseline methods. We also propose several quantitative metrics to further quantify the privacy vulnerability of pre-trained models, which will help the model selection for privacy-sensitive applications. Our code is available at: https://github.com/AI-secure/SecretGen.
We present a non-asymptotic lower bound on the eigenspectrum of the design matrix generated by any linear bandit algorithm with sub-linear regret when the action set has well-behaved curvature. Specifically, we show that the minimum eigenvalue of the expected design matrix grows as $\Omega(\sqrt{n})$ whenever the expected cumulative regret of the algorithm is $O(\sqrt{n})$, where $n$ is the learning horizon, and the action-space has a constant Hessian around the optimal arm. This shows that such action-spaces force a polynomial lower bound rather than a logarithmic lower bound, as shown by \cite{lattimore2017end}, in discrete (i.e., well-separated) action spaces. Furthermore, while the previous result is shown to hold only in the asymptotic regime (as $n \to \infty$), our result for these "locally rich" action spaces is any-time. Additionally, under a mild technical assumption, we obtain a similar lower bound on the minimum eigen value holding with high probability. We apply our result to two practical scenarios -- \emph{model selection} and \emph{clustering} in linear bandits. For model selection, we show that an epoch-based linear bandit algorithm adapts to the true model complexity at a rate exponential in the number of epochs, by virtue of our novel spectral bound. For clustering, we consider a multi agent framework where we show, by leveraging the spectral result, that no forced exploration is necessary -- the agents can run a linear bandit algorithm and estimate their underlying parameters at once, and hence incur a low regret.
Model selection in machine learning (ML) is a crucial part of the Bayesian learning procedure. Model choice may impose strong biases on the resulting predictions, which can hinder the performance of methods such as Bayesian neural networks and neural samplers. On the other hand, newly proposed approaches for Bayesian ML exploit features of approximate inference in function space with implicit stochastic processes (a generalization of Gaussian processes). The approach of Sparse Implicit Processes (SIP) is particularly successful in this regard, since it is fully trainable and achieves flexible predictions. Here, we expand on the original experiments to show that SIP is capable of correcting model bias when the data generating mechanism differs strongly from the one implied by the model. We use synthetic datasets to show that SIP is capable of providing predictive distributions that reflect the data better than the exact predictions of the initial, but wrongly assumed model.
Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this work, we study these statistical and computational trade-offs in variational inference via a case study in inferential model selection. Focusing on Gaussian inferential models (or variational approximating families) with diagonal plus low-rank precision matrices, we initiate a theoretical study of the trade-offs in two aspects, Bayesian posterior inference error and frequentist uncertainty quantification error. From the Bayesian posterior inference perspective, we characterize the error of the variational posterior relative to the exact posterior. We prove that, given a fixed computation budget, a lower-rank inferential model produces variational posteriors with a higher statistical approximation error, but a lower computational error; it reduces variance in stochastic optimization and, in turn, accelerates convergence. From the frequentist uncertainty quantification perspective, we consider the precision matrix of the variational posterior as an uncertainty estimate, which involves an additional statistical error originating from the sampling uncertainty of the data. As a consequence, for small datasets, the inferential model need not be full-rank to achieve optimal estimation error (even with unlimited computation budget).
The model selection procedure is usually a single-criterion decision making in which we select the model that maximizes a specific metric in a specific set, such as the Validation set performance. We claim this is very naive and can perform poor selections of over-fitted models due to the over-searching phenomenon, which over-estimates the performance on that specific set. Futhermore, real world data contains noise that should not be ignored by the model selection procedure and must be taken into account when performing model selection. Also, we have defined four theoretical optimality conditions that we can pursue to better select the models and analyze them by using a multi-criteria decision-making algorithm (TOPSIS) that considers proxies to the optimality conditions to select reasonable models.
How can we collect the most useful labels to learn a model selection policy, when presented with arbitrary heterogeneous data streams? In this paper, we formulate this task as an online contextual active model selection problem, where at each round the learner receives an unlabeled data point along with a context. The goal is to output the best model for any given context without obtaining an excessive amount of labels. In particular, we focus on the task of selecting pre-trained classifiers, and propose a contextual active model selection algorithm (CAMS), which relies on a novel uncertainty sampling query criterion defined on a given policy class for adaptive model selection. In comparison to prior art, our algorithm does not assume a globally optimal model. We provide rigorous theoretical analysis for the regret and query complexity under both adversarial and stochastic settings. Our experiments on several benchmark classification datasets demonstrate the algorithm's effectiveness in terms of both regret and query complexity. Notably, to achieve the same accuracy, CAMS incurs less than 10% of the label cost when compared to the best online model selection baselines on CIFAR10.
Achieving at least some level of explainability requires complex analyses for many machine learning systems, such as common black-box models. We recently proposed a new rule-based learning system, SupRB, to construct compact, interpretable and transparent models by utilizing separate optimizers for the model selection tasks concerning rule discovery and rule set composition.This allows users to specifically tailor their model structure to fulfil use-case specific explainability requirements. From an optimization perspective, this allows us to define clearer goals and we find that -- in contrast to many state of the art systems -- this allows us to keep rule fitnesses independent. In this paper we investigate this system's performance thoroughly on a set of regression problems and compare it against XCSF, a prominent rule-based learning system. We find the overall results of SupRB's evaluation comparable to XCSF's while allowing easier control of model structure and showing a substantially smaller sensitivity to random seeds and data splits. This increased control can aid in subsequently providing explanations for both training and final structure of the model.
Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the approaches used within statistical modelling, the majority of neural network research has been conducted outside of the field of statistics. This has resulted in a lack of statistically-based methodology, and, in particular, there has been little emphasis on model parsimony. Determining the input layer structure is analogous to variable selection, while the structure for the hidden layer relates to model complexity. In practice, neural network model selection is often carried out by comparing models using out-of-sample performance. However, in contrast, the construction of an associated likelihood function opens the door to information-criteria-based variable and architecture selection. A novel model selection method, which performs both input- and hidden-node selection, is proposed using the Bayesian information criterion (BIC) for FNNs. The choice of BIC over out-of-sample performance as the model selection objective function leads to an increased probability of recovering the true model, while parsimoniously achieving favourable out-of-sample performance. Simulation studies are used to evaluate and justify the proposed method, and applications on real data are investigated.
Errors might not have the same consequences depending on the task at hand. Nevertheless, there is limited research investigating the impact of imbalance in the contribution of different features in an error vector. Therefore, we propose the Feature Impact Balance (FIB) score. It measures whether there is a balanced impact of features in the discrepancies between two vectors. We designed the FIB score to lie in [0, 1]. Scores close to 0 indicate that a small number of features contribute to most of the error, and scores close to 1 indicate that most features contribute to the error equally. We experimentally study the FIB on different datasets, using AutoEncoders and Variational AutoEncoders. We show how the feature impact balance varies during training and showcase its usability to support model selection for single output and multi-output tasks.
We consider model selection for classic Reinforcement Learning (RL) environments -- Multi Armed Bandits (MABs) and Markov Decision Processes (MDPs) -- under general function approximations. In the model selection framework, we do not know the function classes, denoted by $\mathcal{F}$ and $\mathcal{M}$, where the true models -- reward generating function for MABs and and transition kernel for MDPs -- lie, respectively. Instead, we are given $M$ nested function (hypothesis) classes such that true models are contained in at-least one such class. In this paper, we propose and analyze efficient model selection algorithms for MABs and MDPs, that \emph{adapt} to the smallest function class (among the nested $M$ classes) containing the true underlying model. Under a separability assumption on the nested hypothesis classes, we show that the cumulative regret of our adaptive algorithms match to that of an oracle which knows the correct function classes (i.e., $\cF$ and $\cM$) a priori. Furthermore, for both the settings, we show that the cost of model selection is an additive term in the regret having weak (logarithmic) dependence on the learning horizon $T$.