Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme that extracts the most informative components for predicting future inputs, termed predictive principal component analysis (PredPCA). Our scheme can effectively remove unpredictable noise and minimize test prediction error through convex optimization. Mathematical analyses demonstrate that, provided with sufficient training samples and sufficiently high-dimensional observations, PredPCA can asymptotically identify hidden states, system parameters, and dimensionalities of canonical nonlinear generative processes, with a global convergence guarantee. We demonstrate the performance of PredPCA using sequential visual inputs comprising hand-digits, rotating 3D objects, and natural scenes. It reliably estimates distinct hidden states and predicts future outcomes of previously unseen test input data, based exclusively on noisy observations. The simple architecture and low computational cost of PredPCA are highly desirable for neuromorphic hardware.
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Shapley values are today extensively used as a model-agnostic explanation framework to explain complex predictive machine learning models. Shapley values have desirable theoretical properties and a sound mathematical foundation in the field of cooperative game theory. Precise Shapley value estimates for dependent data rely on accurate modeling of the dependencies between all feature combinations. In this paper, we use a variational autoencoder with arbitrary conditioning (VAEAC) to model all feature dependencies simultaneously. We demonstrate through comprehensive simulation studies that our VAEAC approach to Shapley value estimation outperforms the state-of-the-art methods for a wide range of settings for both continuous and mixed dependent features. For high-dimensional settings, our VAEAC approach with a non-uniform masking scheme significantly outperforms competing methods. Finally, we apply our VAEAC approach to estimate Shapley value explanations for the Abalone data set from the UCI Machine Learning Repository.
The most common sensing modalities found in a robot perception system are vision and touch, which together can provide global and highly localized data for manipulation. However, these sensing modalities often fail to adequately capture the behavior of target objects during the critical moments as they transition out of static, controlled contact with an end-effector to dynamic and uncontrolled motion. In this work, we present a novel multimodal visuotactile sensor that provides simultaneous visuotactile and proximity depth data. The sensor integrates an RGB camera and air pressure sensor to sense touch with an infrared time-of-flight (ToF) camera to sense proximity by leveraging a selectively transmissive soft membrane to enable the dual sensing modalities. We present the mechanical design, fabrication techniques, algorithm implementations, and evaluation of the sensor's tactile and proximity modalities. The sensor is demonstrated in three open-loop robotic tasks: approaching and contacting an object, catching, and throwing. The fusion of tactile and proximity data could be used to capture key information about a target object's transition behavior for sensor-based control in dynamic manipulation.
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.
Both in scientific literature and in industry,, Semantic and context-aware Natural Language Processing-based solutions have been gaining importance in recent years. The possibilities and performance shown by these models when dealing with complex Language Understanding tasks is unquestionable, from conversational agents to the fight against disinformation in social networks. In addition, considerable attention is also being paid to developing multilingual models to tackle the language bottleneck. The growing need to provide more complex models implementing all these features has been accompanied by an increase in their size, without being conservative in the number of dimensions required. This paper aims to give a comprehensive account of the impact of a wide variety of dimensional reduction techniques on the performance of different state-of-the-art multilingual Siamese Transformers, including unsupervised dimensional reduction techniques such as linear and nonlinear feature extraction, feature selection, and manifold techniques. In order to evaluate the effects of these techniques, we considered the multilingual extended version of Semantic Textual Similarity Benchmark (mSTSb) and two different baseline approaches, one using the pre-trained version of several models and another using their fine-tuned STS version. The results evidence that it is possible to achieve an average reduction in the number of dimensions of $91.58\% \pm 2.59\%$ and $54.65\% \pm 32.20\%$, respectively. This work has also considered the consequences of dimensionality reduction for visualization purposes. The results of this study will significantly contribute to the understanding of how different tuning approaches affect performance on semantic-aware tasks and how dimensional reduction techniques deal with the high-dimensional embeddings computed for the STS task and their potential for highly demanding NLP tasks
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal design criterion, we first obtain a set of optimal subsampling probabilities. Considering that the obtained probabilities are uneconomical, we then propose the nearly optimal ones. With these probabilities, a two step iterative algorithm is established which has lower computational cost and higher accuracy. We provide theoretical analysis and numerical experiments to support the proposed methods. Numerical results demonstrate the decent performance of our methods.
We provide a decision theoretic analysis of bandit experiments. The setting corresponds to a dynamic programming problem, but solving this directly is typically infeasible. Working within the framework of diffusion asymptotics, we define suitable notions of asymptotic Bayes and minimax risk for bandit experiments. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a nonlinear second-order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and non-parametric distribution of the rewards. The approach further describes the state variables it is asymptotically sufficient to restrict attention to, and therefore suggests a practical strategy for dimension reduction. The upshot is that we can approximate the dynamic programming problem defining the bandit experiment with a PDE which can be efficiently solved using sparse matrix routines. We derive the optimal Bayes and minimax policies from the numerical solutions to these equations. The proposed policies substantially dominate existing methods such as Thompson sampling. The framework also allows for substantial generalizations to the bandit problem such as time discounting and pure exploration motives.
We consider M-estimation problems, where the target value is determined using a minimizer of an expected functional of a Levy process. With discrete observations from the Levy process, we can produce a "quasi-path" by shuffling increments of the Levy process, we call it a quasi-process. Under a suitable sampling scheme, a quasi-process can converge weakly to the true process according to the properties of the stationary and independent increments. Using this resampling technique, we can estimate objective functionals similar to those estimated using the Monte Carlo simulations, and it is available as a contrast function. The M-estimator based on these quasi-processes can be consistent and asymptotically normal.
Randomized Maximum Likelihood (RML) is an approximate posterior sampling methodology, widely used in Bayesian inverse problems with complex forward models, particularly in petroleum engineering applications. The procedure involves solving a multi-objective optimization problem, which can be challenging in high-dimensions and when there are constraints on computational costs. We propose a new methodology for tackling the RML optimization problem based on the high-dimensional Bayesian optimization literature. By sharing data between the different objective functions, we are able to implement RML at a greatly reduced computational cost. We demonstrate the benefits of our methodology in comparison with the solutions obtained by alternative optimization methods on a variety of synthetic and real-world problems, including medical and fluid dynamics applications. Furthermore, we show that the samples produced by our method cover well the high-posterior density regions in all of the experiments.
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.
One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.
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