Model selection in contextual bandits is an important complementary problem to regret minimization with respect to a fixed model class. We consider the simplest non-trivial instance of model-selection: distinguishing a simple multi-armed bandit problem from a linear contextual bandit problem. Even in this instance, current state-of-the-art methods explore in a suboptimal manner and require strong "feature-diversity" conditions. In this paper, we introduce new algorithms that a) explore in a data-adaptive manner, and b) provide model selection guarantees of the form $\mathcal{O}(d^{\alpha} T^{1- \alpha})$ with no feature diversity conditions whatsoever, where $d$ denotes the dimension of the linear model and $T$ denotes the total number of rounds. The first algorithm enjoys a "best-of-both-worlds" property, recovering two prior results that hold under distinct distributional assumptions, simultaneously. The second removes distributional assumptions altogether, expanding the scope for tractable model selection. Our approach extends to model selection among nested linear contextual bandits under some additional assumptions.
The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting while preserving desirable properties of the resulting goodness-of-fit (GoF) statistics. In particular, the rank energy (RE) and rank maximum mean discrepancy (RMMD) are distribution-free under the null, exhibit high power in statistical testing, and are robust to outliers. In this paper, we point to and alleviate some of the practical shortcomings of these proposed GoF statistics, namely their high computational cost, high statistical sample complexity, and lack of differentiability with respect to the data. We show that all these practically important issues are addressed by considering entropy-regularized optimal transport maps in place of the rank map, which we refer to as the soft rank. We consequently propose two new statistics, the soft rank energy (sRE) and soft rank maximum mean discrepancy (sRMMD), which exhibit several desirable properties. Given $n$ sample data points, we provide non-asymptotic convergence rates for the sample estimate of the entropic transport map to its population version that are essentially of the order $n^{-1/2}$ when the starting measure is subgaussian and the target measure has compact support. This result is novel compared to existing results which achieve a rate of $n^{-1}$ but crucially rely on both measures having compact support. We leverage this result to demonstrate fast convergence of sample sRE and sRMMD to their population version making them useful for high-dimensional GoF testing. Our statistics are differentiable and amenable to popular machine learning frameworks that rely on gradient methods. We leverage these properties towards showcasing the utility of the proposed statistics for generative modeling on two important problems: image generation and generating valid knockoffs for controlled feature selection.
A practical approach to learning robot skills, often termed sim2real, is to train control policies in simulation and then deploy them on a real robot. Popular techniques to improve the sim2real transfer build on domain randomization (DR) -- training the policy on a diverse set of randomly generated domains with the hope of better generalization to the real world. Due to the large number of hyper-parameters in both the policy learning and DR algorithms, one often ends up with a large number of trained policies, where choosing the best policy among them demands costly evaluation on the real robot. In this work we ask - can we rank the policies without running them in the real world? Our main idea is that a predefined set of real world data can be used to evaluate all policies, using out-of-distribution detection (OOD) techniques. In a sense, this approach can be seen as a `unit test' to evaluate policies before any real world execution. However, we find that by itself, the OOD score can be inaccurate and very sensitive to the particular OOD method. Our main contribution is a simple-yet-effective policy score that combines OOD with an evaluation in simulation. We show that our score - VSDR - can significantly improve the accuracy of policy ranking without requiring additional real world data. We evaluate the effectiveness of VSDR on sim2real transfer in a robotic grasping task with image inputs. We extensively evaluate different DR parameters and OOD methods, and show that VSDR improves policy selection across the board. More importantly, our method achieves significantly better ranking, and uses significantly less data compared to baselines. Project website is available at https://sites.google.com/view/vsdr/home.
We study the problem of learning classifiers that perform well across (known or unknown) groups of data. After observing that common worst-group-accuracy datasets suffer from substantial imbalances, we set out to compare state-of-the-art methods to simple balancing of classes and groups by either subsampling or reweighting data. Our results show that these data balancing baselines achieve state-of-the-art-accuracy, while being faster to train and requiring no additional hyper-parameters. In addition, we highlight that access to group information is most critical for model selection purposes, and not so much during training. All in all, our findings beg closer examination of benchmarks and methods for research in worst-group-accuracy optimization.
Recent progress in model selection raises the question of the fundamental limits of these techniques. Under specific scrutiny has been model selection for general contextual bandits with nested policy classes, resulting in a COLT2020 open problem. It asks whether it is possible to obtain simultaneously the optimal single algorithm guarantees over all policies in a nested sequence of policy classes, or if otherwise this is possible for a trade-off $\alpha\in[\frac{1}{2},1)$ between complexity term and time: $\ln(|\Pi_m|)^{1-\alpha}T^\alpha$. We give a disappointing answer to this question. Even in the purely stochastic regime, the desired results are unobtainable. We present a Pareto frontier of up to logarithmic factors matching upper and lower bounds, thereby proving that an increase in the complexity term $\ln(|\Pi_m|)$ independent of $T$ is unavoidable for general policy classes. As a side result, we also resolve a COLT2016 open problem concerning second-order bounds in full-information games.
Gaussian graphical models provide a powerful framework for uncovering conditional dependence relationships between sets of nodes; they have found applications in a wide variety of fields including sensor and communication networks, physics, finance, and computational biology. Often, one observes data on the nodes and the task is to learn the graph structure, or perform graphical model selection. While this is a well-studied problem with many popular techniques, there are typically three major practical challenges: i) many existing algorithms become computationally intractable in huge-data settings with tens of thousands of nodes; ii) the need for separate data-driven hyperparameter tuning considerably adds to the computational burden; iii) the statistical accuracy of selected edges often deteriorates as the dimension and/or the complexity of the underlying graph structures increase. We tackle these problems by developing the novel Minipatch Graph (MPGraph) estimator. Our approach breaks up the huge graph learning problem into many smaller problems by creating an ensemble of tiny random subsets of both the observations and the nodes, termed minipatches. We then leverage recent advances that use hard thresholding to solve the latent variable graphical model problem to consistently learn the graph on each minipatch. Our approach is computationally fast, embarrassingly parallelizable, memory efficient, and has integrated stability-based hyperparamter tuning. Additionally, we prove that under weaker assumptions than that of the Graphical Lasso, our MPGraph estimator achieves graph selection consistency. We compare our approach to state-of-the-art computational approaches for Gaussian graphical model selection including the BigQUIC algorithm, and empirically demonstrate that our approach is not only more statistically accurate but also extensively faster for huge graph learning problems.
Spatial and spatiotemporal machine-learning models require a suitable framework for their model assessment, model selection, and hyperparameter tuning, in order to avoid error estimation bias and over-fitting. This contribution reviews the state-of-the-art in spatial and spatiotemporal cross-validation, and introduces the {R} package {mlr3spatiotempcv} as an extension package of the machine-learning framework {mlr3}. Currently various {R} packages implementing different spatiotemporal partitioning strategies exist: {blockCV}, {CAST}, {skmeans} and {sperrorest}. The goal of {mlr3spatiotempcv} is to gather the available spatiotemporal resampling methods in {R} and make them available to users through a simple and common interface. This is made possible by integrating the package directly into the {mlr3} machine-learning framework, which already has support for generic non-spatiotemporal resampling methods such as random partitioning. One advantage is the use of a consistent nomenclature in an overarching machine-learning toolkit instead of a varying package-specific syntax, making it easier for users to choose from a variety of spatiotemporal resampling methods. This package avoids giving recommendations which method to use in practice as this decision depends on the predictive task at hand, the autocorrelation within the data, and the spatial structure of the sampling design or geographic objects being studied.
Event-based approaches, which are based on bio-inspired asynchronous event cameras, have achieved promising performance on various computer vision tasks. However, the study of the fundamental event data association problem is still in its infancy. In this paper, we propose a novel Event Data Association (called EDA) approach to explicitly address the event association and fusion problem. The proposed EDA seeks for event trajectories that best fit the event data, in order to perform unifying data association and information fusion. In EDA, we first asynchronously fuse the event data based on its information entropy. Then, we introduce a deterministic model hypothesis generation strategy, which effectively generates model hypotheses from the fused events, to represent the corresponding event trajectories. After that, we present a two-stage weighting algorithm, which robustly weighs and selects true models from the generated model hypotheses, through multi-structural geometric model fitting. Meanwhile, we also propose an adaptive model selection strategy to automatically determine the number of the true models. Finally, we use the selected true models to associate and fuse the event data, without being affected by sensor noise and irrelevant structures. We evaluate the performance of the proposed EDA on the object tracking task. The experimental results show the effectiveness of EDA under challenging scenarios, such as high speed, motion blur, and high dynamic range conditions.
We propose a nested weighted Tchebycheff Multi-objective Bayesian optimization framework where we build a regression model selection procedure from an ensemble of models, towards better estimation of the uncertain parameters of the weighted-Tchebycheff expensive black-box multi-objective function. In existing work, a weighted Tchebycheff MOBO approach has been demonstrated which attempts to estimate the unknown utopia in formulating acquisition function, through calibration using a priori selected regression model. However, the existing MOBO model lacks flexibility in selecting the appropriate regression models given the guided sampled data and therefore, can under-fit or over-fit as the iterations of the MOBO progress, reducing the overall MOBO performance. As it is too complex to a priori guarantee a best model in general, this motivates us to consider a portfolio of different families of predictive models fitted with current training data, guided by the WTB MOBO; the best model is selected following a user-defined prediction root mean-square-error-based approach. The proposed approach is implemented in optimizing a multi-modal benchmark problem and a thin tube design under constant loading of temperature-pressure, with minimizing the risk of creep-fatigue failure and design cost. Finally, the nested weighted Tchebycheff MOBO model performance is compared with different MOBO frameworks with respect to accuracy in parameter estimation, Pareto-optimal solutions and function evaluation cost. This method is generalized enough to consider different families of predictive models in the portfolio for best model selection, where the overall design architecture allows for solving any high-dimensional (multiple functions) complex black-box problems and can be extended to any other global criterion multi-objective optimization methods where prior knowledge of utopia is required.
We introduce three adaptive time series learning methods, called Dynamic Model Selection (DMS), Adaptive Ensemble (AE), and Dynamic Asset Allocation (DAA). The methods respectively handle model selection, ensembling, and contextual evaluation in financial time series. Empirically, we use the methods to forecast the returns of four key indices in the US market, incorporating information from the VIX and Yield curves. We present financial applications of the learning results, including fully-automated portfolios and dynamic hedging strategies. The strategies strongly outperform long-only benchmarks over our testing period, spanning from Q4 2015 to the end of 2021. The key outputs of the learning methods are interpreted during the 2020 market crash.
In Domain Generalization (DG) settings, models trained independently on a given set of training domains have notoriously chaotic performance on distribution shifted test domains, and stochasticity in optimization (e.g. seed) plays a big role. This makes deep learning models unreliable in real world settings. We first show that this chaotic behavior exists even along the training optimization trajectory of a single model, and propose a simple model averaging protocol that both significantly boosts domain generalization and diminishes the impact of stochasticity by improving the rank correlation between the in-domain validation accuracy and out-domain test accuracy, which is crucial for reliable early stopping. Taking advantage of our observation, we show that instead of ensembling unaveraged models (that is typical in practice), ensembling moving average models (EoA) from independent runs further boosts performance. We theoretically explain the boost in performance of ensembling and model averaging by adapting the well known Bias-Variance trade-off to the domain generalization setting. On the DomainBed benchmark, when using a pre-trained ResNet-50, this ensemble of averages achieves an average of $68.0\%$, beating vanilla ERM (w/o averaging/ensembling) by $\sim 4\%$, and when using a pre-trained RegNetY-16GF, achieves an average of $76.6\%$, beating vanilla ERM by $6\%$. Our code is available at \url{https://github.com/salesforce/ensemble-of-averages}.
User interest exploration is an important and challenging topic in recommender systems, which alleviates the closed-loop effects between recommendation models and user-item interactions. Contextual bandit (CB) algorithms strive to make a good trade-off between exploration and exploitation so that users' potential interests have chances to expose. However, classical CB algorithms can only be applied to a small, sampled item set (usually hundreds), which forces the typical applications in recommender systems limited to candidate post-ranking, homepage top item ranking, ad creative selection, or online model selection (A/B test). In this paper, we introduce two simple but effective hierarchical CB algorithms to make a classical CB model (such as LinUCB and Thompson Sampling) capable to explore users' interest in the entire item space without limiting it to a small item set. We first construct a hierarchy item tree via a bottom-up clustering algorithm to organize items in a coarse-to-fine manner. Then we propose a hierarchical CB (HCB) algorithm to explore users' interest in the hierarchy tree. HCB takes the exploration problem as a series of decision-making processes, where the goal is to find a path from the root to a leaf node, and the feedback will be back-propagated to all the nodes in the path. We further propose a progressive hierarchical CB (pHCB) algorithm, which progressively extends visible nodes which reach a confidence level for exploration, to avoid misleading actions on upper-level nodes in the sequential decision-making process. Extensive experiments on two public recommendation datasets demonstrate the effectiveness and flexibility of our methods.
We introduce a new library named abess that implements a unified framework of best-subset selection for solving diverse machine learning problems, e.g., linear regression, classification, and principal component analysis. Particularly, the abess certifiably gets the optimal solution within polynomial times with high probability under the linear model. Our efficient implementation allows abess to attain the solution of best-subset selection problems as fast as or even 20x faster than existing competing variable (model) selection toolboxes. Furthermore, it supports common variants like best group subset selection and $\ell_2$ regularized best-subset selection. The core of the library is programmed in C++. For ease of use, a Python library is designed for conveniently integrating with scikit-learn, and it can be installed from the Python library Index. In addition, a user-friendly R library is available at the Comprehensive R Archive Network. The source code is available at: https://github.com/abess-team/abess.
We theoretically analyze the model selection consistency of least absolute shrinkage and selection operator (Lasso), both with and without post-thresholding, for high-dimensional Ising models. For random regular (RR) graphs of size $p$ with regular node degree $d$ and uniform couplings $\theta_0$, it is rigorously proved that Lasso \textit{without post-thresholding} is model selection consistent in the whole paramagnetic phase with the same order of sample complexity $n=\Omega{(d^3\log{p})}$ as that of $\ell_1$-regularized logistic regression ($\ell_1$-LogR). This result is consistent with the conjecture in Meng, Obuchi, and Kabashima 2021 using the non-rigorous replica method from statistical physics and thus complements it with a rigorous proof. For general tree-like graphs, it is demonstrated that the same result as RR graphs can be obtained under mild assumptions of the dependency condition and incoherence condition. Moreover, we provide a rigorous proof of the model selection consistency of Lasso with post-thresholding for general tree-like graphs in the paramagnetic phase without further assumptions on the dependency and incoherence conditions. Experimental results agree well with our theoretical analysis.
Scaling up model depth and size is now a common approach to raise accuracy in many deep learning (DL) applications, as evidenced by the widespread success of multi-billion or even trillion parameter models in natural language processing (NLP) research. Despite success in DL research and at major technology companies, broader practical adoption of such large models among domain scientists and businesses is still bottlenecked by GPU memory limits, high training costs, and low GPU availability, even on public clouds. Model selection needs further compound these resource challenges: users often need to compare dozens of models with different hyper-parameters or neural architectures to suit their specific task and dataset. In this paper, we present Hydra, a system designed to tackle such challenges by enabling out-of-the-box scaling for multi-large-model DL workloads on even commodity GPUs in a resource-efficient manner. Hydra is the first approach to holistically optimize the execution of multi-model workloads for large DL models. We do this by adapting prior "model-parallel" execution schemes to work with scalable parameter offloading across the memory hierarchy and further hybridizing this approach with task-parallel job scheduling techniques. Hydra decouples scalability of model parameters from parallelism of execution, thus enabling DL users to train even a 6-billion parameter model on a single commodity GPU. It also fully exploits the speedup potential of task parallelism in multi-GPU setups, yielding near-linear strong scaling and making rigorous model selection perhaps more practical for such models. We evaluate end-to-end performance by fine-tuning GPT-2 for language modeling. We find that Hydra offers between 50% and 100% higher training throughput than even the best settings of state-of-the-art industrial frameworks such as DeepSpeed and GPipe for multi-large-model training.
Nanobodies are small antibody fragments derived from camelids that selectively bind to antigens. These proteins have marked physicochemical properties that support advanced therapeutics, including treatments for SARS-CoV-2. To realize their potential, bottom-up proteomics via liquid chromatography-tandem mass spectrometry (LC-MS/MS) has been proposed to identify antigen-specific nanobodies at the proteome scale, where a critical component of this pipeline is matching nanobody peptides to their begotten tandem mass spectra. While peptide-spectrum matching is a well-studied problem, we show the sequence similarity between nanobody peptides violates key assumptions necessary to infer nanobody peptide-spectrum matches (PSMs) with the standard target-decoy paradigm, and prove these violations beget inflated error rates. To address these issues, we then develop a novel framework and method that treats peptide-spectrum matching as a Bayesian model selection problem with an incomplete model space, which are, to our knowledge, the first to account for all sources of PSM error without relying on the aforementioned assumptions. In addition to illustrating our method's improved performance on simulated and real nanobody data, our work demonstrates how to leverage novel retention time and spectrum prediction tools to develop accurate and discriminating data-generating models, and, to our knowledge, provides the first rigorous description of MS/MS spectrum noise.
Recent parameter-efficient language model tuning (PELT) methods manage to match the performance of fine-tuning with much fewer trainable parameters and perform especially well when training data is limited. However, different PELT methods may perform rather differently on the same task, making it nontrivial to select the most appropriate method for a specific task, especially considering the fast-growing number of new PELT methods and tasks. In light of model diversity and the difficulty of model selection, we propose a unified framework, UniPELT, which incorporates different PELT methods as submodules and learns to activate the ones that best suit the current data or task setup via gating mechanism. On the GLUE benchmark, UniPELT consistently achieves 1~4% gains compared to the best individual PELT method that it incorporates and even outperforms fine-tuning under different setups. Moreover, UniPELT generally surpasses the upper bound that takes the best performance of all its submodules used individually on each task, indicating that a mixture of multiple PELT methods may be inherently more effective than single methods.
Materialized model query aims to find the most appropriate materialized model as the initial model for model reuse. It is the precondition of model reuse, and has recently attracted much attention. {Nonetheless, the existing methods suffer from the need to provide source data, limited range of applications, and inefficiency since they do not construct a suitable metric to measure the target-related knowledge of materialized models. To address this, we present \textsf{MMQ}, a source-data free, general, efficient, and effective materialized model query framework.} It uses a Gaussian mixture-based metric called separation degree to rank materialized models. For each materialized model, \textsf{MMQ} first vectorizes the samples in the target dataset into probability vectors by directly applying this model, then utilizes Gaussian distribution to fit for each class of probability vectors, and finally uses separation degree on the Gaussian distributions to measure the target-related knowledge of the materialized model. Moreover, we propose an improved \textsf{MMQ} (\textsf{I-MMQ}), which significantly reduces the query time while retaining the query performance of \textsf{MMQ}. Extensive experiments on a range of practical model reuse workloads demonstrate the effectiveness and efficiency of \textsf{MMQ}.
Electrocorticogram (ECoG) well characterizes hand movement intentions and gestures. In the present work we aim to investigate the possibility to enhance hand pose classification, in a Rock-Paper-Scissor - and Rest - task, by introducing topological descriptors of time series data. We hypothesized that an innovative approach based on topological data analysis can extract hidden information that are not detectable with standard Brain Computer Interface (BCI)techniques. To investigate this hypothesis, we integrate topological features together with power band features and feed them to several standard classifiers, e.g. Random Forest,Gradient Boosting. Model selection is thus completed after a meticulous phase of bayesian hyperparameter optimization. With our method, we observed robust results in terms of ac-curacy for a four-labels classification problem, with limited available data. Through feature importance investigation, we conclude that topological descriptors are able to extract useful discriminative information and provide novel insights.Since our data are restricted to single-patient recordings, generalization might be limited. Nevertheless, our method can be extended and applied to a wide range of neurophysiological recordings and it might be an intriguing point of departure for future studies.
Principal component analysis (PCA) has been widely used as an effective technique for feature extraction and dimension reduction. In the High Dimension Low Sample Size (HDLSS) setting, one may prefer modified principal components, with penalized loadings, and automated penalty selection by implementing model selection among these different models with varying penalties. The earlier work [1, 2] has proposed penalized PCA, indicating the feasibility of model selection in $L_2$- penalized PCA through the solution path of Ridge regression, however, it is extremely time-consuming because of the intensive calculation of matrix inverse. In this paper, we propose a fast model selection method for penalized PCA, named Approximated Gradient Flow (AgFlow), which lowers the computation complexity through incorporating the implicit regularization effect introduced by (stochastic) gradient flow [3, 4] and obtains the complete solution path of $L_2$-penalized PCA under varying $L_2$-regularization. We perform extensive experiments on real-world datasets. AgFlow outperforms existing methods (Oja [5], Power [6], and Shamir [7] and the vanilla Ridge estimators) in terms of computation costs.