We consider the problem of constructing minimax rate-optimal estimators for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. Minimax rate-optimal estimators for such functionals are typically constructed through higher-order bias corrections of plug-in and one-step type estimators and, in turn, depend on estimators of nuisance functions. In this paper, we consider a parallel question of interest regarding the optimality and/or sub-optimality of plug-in and one-step bias-corrected estimators for the specific doubly robust functional of interest. Specifically, we verify that by using undersmoothing and sample splitting techniques when constructing nuisance function estimators, one can achieve minimax rates of convergence in all H\"older smoothness classes of the nuisance functions (i.e. the propensity score and outcome regression) provided that the marginal density of the covariates is sufficiently regular. Additionally, by demonstrating suitable lower bounds on these classes of estimators, we demonstrate the necessity to undersmooth the nuisance function estimators to obtain minimax optimal rates of convergence.

In this paper, we consider the problem of adjusting the exploration rate when using value-of-information-based exploration. We do this by converting the value-of-information optimization into a problem of finding equilibria of a flow for a changing exploration rate. We then develop an efficient path-following scheme for converging to these equilibria and hence uncovering optimal action-selection policies. Under this scheme, the exploration rate is automatically adapted according to the agent's experiences. Global convergence is theoretically assured. We first evaluate our exploration-rate adaptation on the Nintendo GameBoy games Centipede and Millipede. We demonstrate aspects of the search process, like that it yields a hierarchy of state abstractions. We also show that our approach returns better policies in fewer episodes than conventional search strategies relying on heuristic, annealing-based exploration-rate adjustments. We then illustrate that these trends hold for deep, value-of-information-based agents that learn to play ten simple games and over forty more complicated games for the Nintendo GameBoy system. Performance either near or well above the level of human play is observed.

Objective: Convolutional neural networks (CNNs) have demonstrated promise in automated cardiac magnetic resonance image segmentation. However, when using CNNs in a large real-world dataset, it is important to quantify segmentation uncertainty and identify segmentations which could be problematic. In this work, we performed a systematic study of Bayesian and non-Bayesian methods for estimating uncertainty in segmentation neural networks. Methods: We evaluated Bayes by Backprop, Monte Carlo Dropout, Deep Ensembles, and Stochastic Segmentation Networks in terms of segmentation accuracy, probability calibration, uncertainty on out-of-distribution images, and segmentation quality control. Results: We observed that Deep Ensembles outperformed the other methods except for images with heavy noise and blurring distortions. We showed that Bayes by Backprop is more robust to noise distortions while Stochastic Segmentation Networks are more resistant to blurring distortions. For segmentation quality control, we showed that segmentation uncertainty is correlated with segmentation accuracy for all the methods. With the incorporation of uncertainty estimates, we were able to reduce the percentage of poor segmentation to 5% by flagging 31--48% of the most uncertain segmentations for manual review, substantially lower than random review without using neural network uncertainty (reviewing 75--78% of all images). Conclusion: This work provides a comprehensive evaluation of uncertainty estimation methods and showed that Deep Ensembles outperformed other methods in most cases. Significance: Neural network uncertainty measures can help identify potentially inaccurate segmentations and alert users for manual review.

The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity. In some sequential estimation problems however, the future values of the quantity to be estimated depend on the estimate of its current value. This type of estimation problems has been formulated as the dynamic inference problem. In this work, we formulate the Bayesian learning problem for dynamic inference, where the unknown quantity-generation model is assumed to be randomly drawn according to a random model parameter. We derive the optimal Bayesian learning rules, both offline and online, to minimize the inference loss. Moreover, learning for dynamic inference can serve as a meta problem, such that all familiar machine learning problems, including supervised learning, imitation learning and reinforcement learning, can be cast as its special cases or variants. Gaining a good understanding of this unifying meta problem thus sheds light on a broad spectrum of machine learning problems as well.

In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian-Like error bound for such systems, 3) discuss various consequences of this error bound.

You tagged this question with the tag "Maximum Likelihood". In maximum likelihood estimation you explicitly maximize an objective function (namely the likelihood). It just so happens that for an observation that we assume to be drawn from a Gaussian random variable, the likelihood function usually takes a nice form after you take a logarithm. Then there is usually a leading negation, encouraging the entrepreneurial optimizer to switch away from maximizing the objective to minimizing the negative of objective, or roughly the "cost". For discrete maximum likelihood estimation the "cost" also has another meaningful name since it takes the same form as the euclidean distance in the observation space.

Denoising Diffusion Probabilistic Models (DDPMs) are emerging in text-to-speech (TTS) synthesis because of their strong capability of generating high-fidelity samples. However, their iterative refinement process in high-dimensional data space results in slow inference speed, which restricts their application in real-time systems. Previous works have explored speeding up by minimizing the number of inference steps but at the cost of sample quality. In this work, to improve the inference speed for DDPM-based TTS model while achieving high sample quality, we propose ResGrad, a lightweight diffusion model which learns to refine the output spectrogram of an existing TTS model (e.g., FastSpeech 2) by predicting the residual between the model output and the corresponding ground-truth speech. ResGrad has several advantages: 1) Compare with other acceleration methods for DDPM which need to synthesize speech from scratch, ResGrad reduces the complexity of task by changing the generation target from ground-truth mel-spectrogram to the residual, resulting into a more lightweight model and thus a smaller real-time factor. 2) ResGrad is employed in the inference process of the existing TTS model in a plug-and-play way, without re-training this model. We verify ResGrad on the single-speaker dataset LJSpeech and two more challenging datasets with multiple speakers (LibriTTS) and high sampling rate (VCTK). Experimental results show that in comparison with other speed-up methods of DDPMs: 1) ResGrad achieves better sample quality with the same inference speed measured by real-time factor; 2) with similar speech quality, ResGrad synthesizes speech faster than baseline methods by more than 10 times. Audio samples are available at https://resgrad1.github.io/.

A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This fragmentation of goals causes not only an inconsistent conceptual understanding of explanations but also the practical challenge of not knowing which method to use when. In this work, we begin to address these challenges by unifying eight popular post hoc explanation methods (LIME, C-LIME, KernelSHAP, Occlusion, Vanilla Gradients, Gradients x Input, SmoothGrad, and Integrated Gradients). We show that these methods all perform local function approximation of the black-box model, differing only in the neighbourhood and loss function used to perform the approximation. This unification enables us to (1) state a no free lunch theorem for explanation methods, demonstrating that no method can perform optimally across all neighbourhoods, and (2) provide a guiding principle to choose among methods based on faithfulness to the black-box model. We empirically validate these theoretical results using various real-world datasets, model classes, and prediction tasks. By bringing diverse explanation methods into a common framework, this work (1) advances the conceptual understanding of these methods, revealing their shared local function approximation objective, properties, and relation to one another, and (2) guides the use of these methods in practice, providing a principled approach to choose among methods and paving the way for the creation of new ones.

Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the effect of variance are regularized estimators, shrinkage estimators and Bayesian estimation. In the current work we investigate the latter two solutions, which have not yet been applied to subspace identification. Our experimental results show that our proposed estimators may reduce the estimation risk up to $40\%$ of that of traditional subspace methods.

Rapid advancements in collection, processing, and dissemination of multi-platform molecular and genomics (multi-omics, in short) data has resulted in enormous opportunities to aggregate such data in order to understand, prevent, and treat diseases. This has catalyzed development of integrative methods that can collectively mine multiple types and scales of multi-omics data, in order to provide a more holistic view of human disease evolution and progression (Subramanian et al. 2020). Specifically, in the context of cancer, a disease driven predominantly by agglomerations of several molecular changes (Sun et al. 2021), the importance of synthesizing information from multi-platform omics and clinical sources to understand the cellular basis of the disease is even further underscored. Cellular oncological mechanisms, triggered at different molecular levels of the DNA RNA Protein path, can confer profound phenotypic advantages/disadvantages. While significant improvements have been made in multi-omics data integration methods to unveil such mechanisms, focused on both prognosis (Duan et al. 2021) and treatment (Finotello et al. 2020), the precise functions governing them need detailed and data-driven de-novo evaluations. Our work, in the same vein, aims at two different but inter-related scientific axes: (i) selection of biomarkers associated with cancer prognosis and clinical outcomes, and (ii) learning the mechanism of these biomarkers' effects upon such outcomes via integrating upstream molecular information - we provide some additional scientific context below. Classes of Integrative Omics Models First, we briefly discuss existing integrative omics approaches in order to contextualize the need for our framework. Broadly, most of the existing integrative statistical methods can be classified into two categories - horizontal (meta-analysis type) and vertical (multi-omics) integration procedures (Tseng et al. 2015).