A primary goal of modern cancer research is to characterize tumour growth and evolution, to improve clinical forecasting and individualized treatment. Agent-based models support this endeavour but existing models either oversimplify spatial structure or are mathematically intractable. Here we present warlock, an open-source automated computational workflow for fast, efficient simulation of intratumour population genetics in any of a diverse set of spatial structures. Warlock encapsulates a deme-based oncology model (demon), designed to bridge the divide between agent-based simulations and analytical population genetics models, such as the spatial Moran process. Model output can be readily compared to multi-region and single-cell sequencing data for model selection or biological parameter inference. An interface for High Performance Computing permits hundreds of simulations to be run in parallel. We discuss prior applications of this workflow to investigating human cancer evolution.
We propose data thinning, an approach for splitting an observation into two or more independent parts that sum to the original observation, and that follow the same distribution as the original observation, up to a (known) scaling of a parameter. This very general proposal is applicable to any convolution-closed distribution, a class that includes the Gaussian, Poisson, negative binomial, gamma, and binomial distributions, among others. Data thinning has a number of applications to model selection, evaluation, and inference. For instance, cross-validation via data thinning provides an attractive alternative to the usual approach of cross-validation via sample splitting, especially in settings in which the latter is not applicable. In simulations and in an application to single-cell RNA-sequencing data, we show that data thinning can be used to validate the results of unsupervised learning approaches, such as k-means clustering and principal components analysis, for which traditional sample splitting is unattractive or unavailable.
Deep Neural Networks are increasingly adopted in critical tasks that require a high level of safety, e.g., autonomous driving. While state-of-the-art verifiers can be employed to check whether a DNN is unsafe w.r.t. some given property (i.e., whether there is at least one unsafe input configuration), their yes/no output is not informative enough for other purposes, such as shielding, model selection, or training improvements. In this paper, we introduce the #DNN-Verification problem, which involves counting the number of input configurations of a DNN that result in a violation of a particular safety property. We analyze the complexity of this problem and propose a novel approach that returns the exact count of violations. Due to the #P-completeness of the problem, we also propose a randomized, approximate method that provides a provable probabilistic bound of the correct count while significantly reducing computational requirements. We present experimental results on a set of safety-critical benchmarks that demonstrate the effectiveness of our approximate method and evaluate the tightness of the bound.
In-context learning (ICL) is a type of prompting where a transformer model operates on a sequence of (input, output) examples and performs inference on-the-fly. In this work, we formalize in-context learning as an algorithm learning problem where a transformer model implicitly constructs a hypothesis function at inference-time. We first explore the statistical aspects of this abstraction through the lens of multitask learning: We obtain generalization bounds for ICL when the input prompt is (1) a sequence of i.i.d. (input, label) pairs or (2) a trajectory arising from a dynamical system. The crux of our analysis is relating the excess risk to the stability of the algorithm implemented by the transformer. We characterize when transformer/attention architecture provably obeys the stability condition and also provide empirical verification. For generalization on unseen tasks, we identify an inductive bias phenomenon in which the transfer learning risk is governed by the task complexity and the number of MTL tasks in a highly predictable manner. Finally, we provide numerical evaluations that (1) demonstrate transformers can indeed implement near-optimal algorithms on classical regression problems with i.i.d. and dynamic data, (2) provide insights on stability, and (3) verify our theoretical predictions.
We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. Recently, Guo et al. (2020) showed that the model selection performance of BSS depends on a certain identifiability margin, a measure that captures the model discriminative power of BSS under a general correlation structure that is robust to the design dependence, unlike its computational surrogates such as LASSO, SCAD, MCP, etc. Expanding on this, we further broaden the theoretical understanding of best subset selection in this paper and show that the complexities of the residualized signals, the portion of the signals orthogonal to the true active features, and spurious projections, describing the projection operators associated with the irrelevant features, also play fundamental roles in characterizing the margin condition for model consistency of BSS. In particular, we establish both necessary and sufficient margin conditions depending only on the identifiability margin and the two complexity measures. We also partially extend our sufficiency result to the case of high-dimensional sparse generalized linear models (GLMs).
Evaluating policy in imperfectly competitive markets requires understanding firm behavior. While researchers test conduct via model selection and assessment, we present advantages of Rivers and Vuong (2002) (RV) model selection under misspecification. However, degeneracy of RV invalidates inference. With a novel definition of weak instruments for testing, we connect degeneracy to instrument strength, derive weak instrument properties of RV, and provide a diagnostic for weak instruments by extending the framework of Stock and Yogo (2005) to model selection. We test vertical conduct (Villas-Boas, 2007) using common instrument sets. Some are weak, providing no power. Strong instruments support manufacturers setting retail prices.
Data organized in tabular format is ubiquitous in real-world applications, and users often craft tables with biased feature definitions and flexibly set prediction targets of their interests. Thus, a rapid development of a robust, effective, dataset-versatile, user-friendly tabular prediction approach is highly desired. While Gradient Boosting Decision Trees (GBDTs) and existing deep neural networks (DNNs) have been extensively utilized by professional users, they present several challenges for casual users, particularly: (i) the dilemma of model selection due to their different dataset preferences, and (ii) the need for heavy hyperparameter searching, failing which their performances are deemed inadequate. In this paper, we delve into this question: Can we develop a deep learning model that serves as a "sure bet" solution for a wide range of tabular prediction tasks, while also being user-friendly for casual users? We delve into three key drawbacks of deep tabular models, encompassing: (P1) lack of rotational variance property, (P2) large data demand, and (P3) over-smooth solution. We propose ExcelFormer, addressing these challenges through a semi-permeable attention module that effectively constrains the influence of less informative features to break the DNNs' rotational invariance property (for P1), data augmentation approaches tailored for tabular data (for P2), and attentive feedforward network to boost the model fitting capability (for P3). These designs collectively make ExcelFormer a "sure bet" solution for diverse tabular datasets. Extensive and stratified experiments conducted on real-world datasets demonstrate that our model outperforms previous approaches across diverse tabular data prediction tasks, and this framework can be friendly to casual users, offering ease of use without the heavy hyperparameter tuning.
The application of deep learning to non-stationary temporal datasets can lead to overfitted models that underperform under regime changes. In this work, we propose a modular machine learning pipeline for ranking predictions on temporal panel datasets which is robust under regime changes. The modularity of the pipeline allows the use of different models, including Gradient Boosting Decision Trees (GBDTs) and Neural Networks, with and without feature engineering. We evaluate our framework on financial data for stock portfolio prediction, and find that GBDT models with dropout display high performance, robustness and generalisability with reduced complexity and computational cost. We then demonstrate how online learning techniques, which require no retraining of models, can be used post-prediction to enhance the results. First, we show that dynamic feature projection improves robustness by reducing drawdown in regime changes. Second, we demonstrate that dynamical model ensembling based on selection of models with good recent performance leads to improved Sharpe and Calmar ratios of out-of-sample predictions. We also evaluate the robustness of our pipeline across different data splits and random seeds with good reproducibility.
We present a Machine Learning (ML) study case to illustrate the challenges of clinical translation for a real-time AI-empowered echocardiography system with data of ICU patients in LMICs. Such ML case study includes data preparation, curation and labelling from 2D Ultrasound videos of 31 ICU patients in LMICs and model selection, validation and deployment of three thinner neural networks to classify apical four-chamber view. Results of the ML heuristics showed the promising implementation, validation and application of thinner networks to classify 4CV with limited datasets. We conclude this work mentioning the need for (a) datasets to improve diversity of demographics, diseases, and (b) the need of further investigations of thinner models to be run and implemented in low-cost hardware to be clinically translated in the ICU in LMICs. The code and other resources to reproduce this work are available at https://github.com/vital-ultrasound/ai-assisted-echocardiography-for-low-resource-countries.
Characterizing how neural network depth, width, and dataset size jointly impact model quality is a central problem in deep learning theory. We give here a complete solution in the special case of linear networks with output dimension one trained using zero noise Bayesian inference with Gaussian weight priors and mean squared error as a negative log-likelihood. For any training dataset, network depth, and hidden layer widths, we find non-asymptotic expressions for the predictive posterior and Bayesian model evidence in terms of Meijer-G functions, a class of meromorphic special functions of a single complex variable. Through novel asymptotic expansions of these Meijer-G functions, a rich new picture of the joint role of depth, width, and dataset size emerges. We show that linear networks make provably optimal predictions at infinite depth: the posterior of infinitely deep linear networks with data-agnostic priors is the same as that of shallow networks with evidence-maximizing data-dependent priors. This yields a principled reason to prefer deeper networks when priors are forced to be data-agnostic. Moreover, we show that with data-agnostic priors, Bayesian model evidence in wide linear networks is maximized at infinite depth, elucidating the salutary role of increased depth for model selection. Underpinning our results is a novel emergent notion of effective depth, given by the number of hidden layers times the number of data points divided by the network width; this determines the structure of the posterior in the large-data limit.
Selecting the number of topics in LDA models is considered to be a difficult task, for which alternative approaches have been proposed. The performance of the recently developed singular Bayesian information criterion (sBIC) is evaluated and compared to the performance of alternative model selection criteria. The sBIC is a generalization of the standard BIC that can be implemented to singular statistical models. The comparison is based on Monte Carlo simulations and carried out for several alternative settings, varying with respect to the number of topics, the number of documents and the size of documents in the corpora. Performance is measured using different criteria which take into account the correct number of topics, but also whether the relevant topics from the DGPs are identified. Practical recommendations for LDA model selection in applications are derived.
G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the Minimum Description Length principle (MDL) to derive two different model selection criteria. Several proven theoretical results about these criteria give insights about their asymptotic behavior and are used to speed up their optimisation. These insights, combined to a greedy search heuristic, are used to construct histograms in linearithmic time rather than the polynomial time incurred by previous works. The capabilities of the proposed MDL density estimation method are illustrated with reference to other fully automated methods in the literature, both on synthetic and large real-world data sets.
Autonomous mobile agents such as unmanned aerial vehicles (UAVs) and mobile robots have shown huge potential for improving human productivity. These mobile agents require low power/energy consumption to have a long lifespan since they are usually powered by batteries. These agents also need to adapt to changing/dynamic environments, especially when deployed in far or dangerous locations, thus requiring efficient online learning capabilities. These requirements can be fulfilled by employing Spiking Neural Networks (SNNs) since SNNs offer low power/energy consumption due to sparse computations and efficient online learning due to bio-inspired learning mechanisms. However, a methodology is still required to employ appropriate SNN models on autonomous mobile agents. Towards this, we propose a Mantis methodology to systematically employ SNNs on autonomous mobile agents to enable energy-efficient processing and adaptive capabilities in dynamic environments. The key ideas of our Mantis include the optimization of SNN operations, the employment of a bio-plausible online learning mechanism, and the SNN model selection. The experimental results demonstrate that our methodology maintains high accuracy with a significantly smaller memory footprint and energy consumption (i.e., 3.32x memory reduction and 2.9x energy saving for an SNN model with 8-bit weights) compared to the baseline network with 32-bit weights. In this manner, our Mantis enables the employment of SNNs for resource- and energy-constrained mobile agents.
Task transfer learning is a popular technique in image processing applications that uses pre-trained models to reduce the supervision cost of related tasks. An important question is to determine task transferability, i.e. given a common input domain, estimating to what extent representations learned from a source task can help in learning a target task. Typically, transferability is either measured experimentally or inferred through task relatedness, which is often defined without a clear operational meaning. In this paper, we present a novel metric, H-score, an easily-computable evaluation function that estimates the performance of transferred representations from one task to another in classification problems using statistical and information theoretic principles. Experiments on real image data show that our metric is not only consistent with the empirical transferability measurement, but also useful to practitioners in applications such as source model selection and task transfer curriculum learning.
Recently, many causal estimators for Conditional Average Treatment Effect (CATE) and instrumental variable (IV) problems have been published and open sourced, allowing to estimate granular impact of both randomized treatments (such as A/B tests) and of user choices on the outcomes of interest. However, the practical application of such models has ben hampered by the lack of a valid way to score the performance of such models out of sample, in order to select the best one for a given application. We address that gap by proposing novel scoring approaches for both the CATE case and an important subset of instrumental variable problems, namely those where the instrumental variable is customer acces to a product feature, and the treatment is the customer's choice to use that feature. Being able to score model performance out of sample allows us to apply hyperparameter optimization methods to causal model selection and tuning. We implement that in an open source package that relies on DoWhy and EconML libraries for implementation of causal inference models (and also includes a Transformed Outcome model implementation), and on FLAML for hyperparameter optimization and for component models used in the causal models. We demonstrate on synthetic data that optimizing the proposed scores is a reliable method for choosing the model and its hyperparameter values, whose estimates are close to the true impact, in the randomized CATE and IV cases. Further, we provide examles of applying these methods to real customer data from Wise.
In contextual linear bandits, the reward function is assumed to be a linear combination of an unknown reward vector and a given embedding of context-arm pairs. In practice, the embedding is often learned at the same time as the reward vector, thus leading to an online representation learning problem. Existing approaches to representation learning in contextual bandits are either very generic (e.g., model-selection techniques or algorithms for learning with arbitrary function classes) or specialized to particular structures (e.g., nested features or representations with certain spectral properties). As a result, the understanding of the cost of representation learning in contextual linear bandit is still limited. In this paper, we take a systematic approach to the problem and provide a comprehensive study through an instance-dependent perspective. We show that representation learning is fundamentally more complex than linear bandits (i.e., learning with a given representation). In particular, learning with a given set of representations is never simpler than learning with the worst realizable representation in the set, while we show cases where it can be arbitrarily harder. We complement this result with an extensive discussion of how it relates to existing literature and we illustrate positive instances where representation learning is as complex as learning with a fixed representation and where sub-logarithmic regret is achievable.
For western economies a long-forgotten phenomenon is on the horizon: rising inflation rates. We propose a novel approach christened D2ML to identify drivers of national inflation. D2ML combines machine learning for model selection with time dependent data and graphical models to estimate the inverse of the covariance matrix, which is then used to identify dominant drivers. Using a dataset of 33 countries, we find that the US inflation rate and oil prices are dominant drivers of national inflation rates. For a more general framework, we carry out Monte Carlo simulations to show that our estimator correctly identifies dominant drivers.
We propose a new model-selection algorithm for Regression Discontinuity Design, Regression Kink Design, and related IV estimators. Candidate models are assessed within a 'placebo zone' of the running variable, where the true effects are known to be zero. The approach yields an optimal combination of bandwidth, polynomial, and any other choice parameters. It can also inform choices between classes of models (e.g. RDD versus cohort-IV) and any other choices, such as covariates, kernel, or other weights. We outline sufficient conditions under which the approach is asymptotically optimal. The approach also performs favorably under more general conditions in a series of Monte Carlo simulations. We demonstrate the approach in an evaluation of changes to Minimum Supervised Driving Hours in the Australian state of New South Wales. We also re-evaluate evidence on the effects of Head Start and Minimum Legal Drinking Age. Our Stata commands implement the procedure and compare its performance to other approaches.
This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e., those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. arm). We study a particular case of the rested and restless bandits in which the arms' expected payoff is monotonically non-decreasing. This characteristic allows designing specifically crafted algorithms that exploit the regularity of the payoffs to provide tight regret bounds. We design an algorithm for the rested case (R-ed-UCB) and one for the restless case (R-less-UCB), providing a regret bound depending on the properties of the instance and, under certain circumstances, of $\widetilde{\mathcal{O}}(T^{\frac{2}{3}})$. We empirically compare our algorithms with state-of-the-art methods for non-stationary MABs over several synthetically generated tasks and an online model selection problem for a real-world dataset. Finally, using synthetic and real-world data, we illustrate the effectiveness of the proposed approaches compared with state-of-the-art algorithms for the non-stationary bandits.
Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. This paper presents a robust multi-fidelity surrogate modeling strategy in which the multi-fidelity surrogate is assembled using an active learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework for efficient reliability analysis. The multi-fidelity surrogate is assembled by first applying a Gaussian process correction to each low-fidelity model and assigning a model probability based on the model's local predictive accuracy and cost. Three strategies are proposed to fuse these individual surrogates into an overall surrogate model based on model averaging and deterministic/stochastic model selection. The strategies also dictate which model evaluations are necessary. No assumptions are made about the relationships between low-fidelity models, while the high-fidelity model is assumed to be the most accurate and most computationally expensive model. Through two analytical and two numerical case studies, including a case study evaluating the failure probability of Tristructural isotropic-coated (TRISO) nuclear fuels, the algorithm is shown to be highly accurate while drastically reducing the number of high-fidelity model calls (and hence computational cost).