Identifiability of latent variable models has recently gained interest in terms of its applications to interpretability or out of distribution generalisation. In this work, we study identifiability of Markov Switching Models as a first step towards extending recent results to sequential latent variable models. We present identifiability conditions within first-order Markov dependency structures, and parametrise the transition distribution via non-linear Gaussians. Our experiments showcase the applicability of our approach for regime-dependent causal discovery and high-dimensional time series segmentation.
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Topological data analysis (TDA) has emerged as a powerful tool for extracting meaningful insights from complex data. TDA enhances the analysis of objects by embedding them into a simplicial complex and extracting useful global properties such as the Betti numbers, i.e. the number of multidimensional holes, which can be used to define kernel methods that are easily integrated with existing machine-learning algorithms. These kernel methods have found broad applications, as they rely on powerful mathematical frameworks which provide theoretical guarantees on their performance. However, the computation of higher-dimensional Betti numbers can be prohibitively expensive on classical hardware, while quantum algorithms can approximate them in polynomial time in the instance size. In this work, we propose a quantum approach to defining topological kernels, which is based on constructing Betti curves, i.e. topological fingerprint of filtrations with increasing order. We exhibit a working prototype of our approach implemented on a noiseless simulator and show its robustness by means of some empirical results suggesting that topological approaches may offer an advantage in quantum machine learning.
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing the Hamiltonian, for which a classical algorithm typically requires a computational complexity that scales cubically with respect to the number of electrons. This limits DFT's applicability to large-scale problems with complex chemical environments and microstructures. This article presents a quantum algorithm that has a linear scaling with respect to the number of atoms, which is much smaller than the number of electrons. Our algorithm leverages the quantum singular value transformation (QSVT) to generate a quantum circuit to encode the density-matrix, and an estimation method for computing the output electron density. In addition, we present a randomized block coordinate fixed-point method to accelerate the self-consistent field calculations by reducing the number of components of the electron density that needs to be estimated. The proposed framework is accompanied by a rigorous error analysis that quantifies the function approximation error, the statistical fluctuation, and the iteration complexity. In particular, the analysis of our self-consistent iterations takes into account the measurement noise from the quantum circuit. These advancements offer a promising avenue for tackling large-scale DFT problems, enabling simulations of complex systems that were previously computationally infeasible.
Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within clusters, is mostly fixed in advance, in the recent literature models with automatic inference on both the number of clusters and latent factors have been introduced. The automatic inference is usually done by assigning a nonparametric prior and allowing the number of clusters and factors to potentially go to infinity. The MCMC estimation is performed via an adaptive algorithm, in which the parameters associated with the redundant factors are discarded as the chain moves. While this approach has clear advantages, it also bears some significant drawbacks. Running a separate factor-analytical model for each cluster involves matrices of changing dimensions, which can make the model and programming somewhat cumbersome. In addition, discarding the parameters associated with the redundant factors could lead to a bias in estimating cluster covariance matrices. At last, identification remains problematic for infinite factor models. The current work contributes to the MFA literature by providing for the automatic inference on the number of clusters and the number of cluster-specific factors while keeping both cluster and factor dimensions finite. This allows us to avoid many of the aforementioned drawbacks of the infinite models. For the automatic inference on the cluster structure, we employ the dynamic mixture of finite mixtures (MFM) model. Automatic inference on cluster-specific factors is performed by assigning an exchangeable shrinkage process (ESP) prior to the columns of the factor loading matrices. The performance of the model is demonstrated on several benchmark data sets as well as real data applications.
I consider a class of statistical decision problems in which the policy maker must decide between two alternative policies to maximize social welfare based on a finite sample. The central assumption is that the underlying, possibly infinite-dimensional parameter, lies in a known convex set, potentially leading to partial identification of the welfare effect. An example of such restrictions is the smoothness of counterfactual outcome functions. As the main theoretical result, I derive a finite-sample, exact minimax regret decision rule within the class of all decision rules under normal errors with known variance. When the error distribution is unknown, I obtain a feasible decision rule that is asymptotically minimax regret. I apply my results to the problem of whether to change a policy eligibility cutoff in a regression discontinuity setup, and illustrate them in an empirical application to a school construction program in Burkina Faso.
This paper explores the integration of Large Language Models (LLMs) into Automatic Speech Recognition (ASR) systems to improve transcription accuracy. The increasing sophistication of LLMs, with their in-context learning capabilities and instruction-following behavior, has drawn significant attention in the field of Natural Language Processing (NLP). Our primary focus is to investigate the potential of using an LLM's in-context learning capabilities to enhance the performance of ASR systems, which currently face challenges such as ambient noise, speaker accents, and complex linguistic contexts. We designed a study using the Aishell-1 and LibriSpeech datasets, with ChatGPT and GPT-4 serving as benchmarks for LLM capabilities. Unfortunately, our initial experiments did not yield promising results, indicating the complexity of leveraging LLM's in-context learning for ASR applications. Despite further exploration with varied settings and models, the corrected sentences from the LLMs frequently resulted in higher Word Error Rates (WER), demonstrating the limitations of LLMs in speech applications. This paper provides a detailed overview of these experiments, their results, and implications, establishing that using LLMs' in-context learning capabilities to correct potential errors in speech recognition transcriptions is still a challenging task at the current stage.
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.
Attention Model has now become an important concept in neural networks that has been researched within diverse application domains. This survey provides a structured and comprehensive overview of the developments in modeling attention. In particular, we propose a taxonomy which groups existing techniques into coherent categories. We review the different neural architectures in which attention has been incorporated, and also show how attention improves interpretability of neural models. Finally, we discuss some applications in which modeling attention has a significant impact. We hope this survey will provide a succinct introduction to attention models and guide practitioners while developing approaches for their applications.
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