We introduce an information-theoretic method for quantifying causality in chaotic systems. The approach, referred to as IT-causality, quantifies causality by measuring the information gained about future events conditioned on the knowledge of past events. The causal interactions are classified into redundant, unique, and synergistic contributions depending on their nature. The formulation is non-intrusive, invariance under invertible transformations of the variables, and provides the missing causality due to unobserved variables. The method only requires pairs of past-future events of the quantities of interest, making it convenient for both computational simulations and experimental investigations. IT-causality is validated in four scenarios representing basic causal interactions among variables: mediator, confounder, redundant collider, and synergistic collider. The approach is leveraged to address two questions relevant to turbulence research: i) the scale locality of the energy cascade in isotropic turbulence, and ii) the interactions between inner and outer layer flow motions in wall-bounded turbulence. In the former case, we demonstrate that causality in the energy cascade flows sequentially from larger to smaller scales without requiring intermediate scales. Conversely, the flow of information from small to large scales is shown to be redundant. In the second problem, we observe a unidirectional causality flow, with causality predominantly originating from the outer layer and propagating towards the inner layer, but not vice versa. The decomposition of IT-causality into intensities also reveals that the causality is primarily associated with high-velocity streaks.
相關內容
IFIP TC13 Conference on Human-Computer Interaction是人機交互領域的研究者和實踐者展示其工作的重要平臺。多年來，這些會議吸引了來自幾個國家和文化的研究人員。官網鏈接： ·
Extensibility
·
MoDELS
·
state-of-the-art
·
講稿
·
We present ParrotTTS, a modularized text-to-speech synthesis model leveraging disentangled self-supervised speech representations. It can train a multi-speaker variant effectively using transcripts from a single speaker. ParrotTTS adapts to a new language in low resource setup and generalizes to languages not seen while training the self-supervised backbone. Moreover, without training on bilingual or parallel examples, ParrotTTS can transfer voices across languages while preserving the speaker specific characteristics, e.g., synthesizing fluent Hindi speech using a French speaker's voice and accent. We present extensive results in monolingual and multi-lingual scenarios. ParrotTTS outperforms state-of-the-art multi-lingual TTS models using only a fraction of paired data as latter.
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are held fixed. We consider a family of BMM algorithms for minimizing smooth nonconvex objectives, where each parameter block is constrained within a subset of a Riemannian manifold. We establish that this algorithm converges asymptotically to the set of stationary points, and attains an $\epsilon$-stationary point within $\widetilde{O}(\epsilon^{-2})$ iterations. In particular, the assumptions for our complexity results are completely Euclidean when the underlying manifold is a product of Euclidean or Stiefel manifolds, although our analysis makes explicit use of the Riemannian geometry. Our general analysis applies to a wide range of algorithms with Riemannian constraints: Riemannian MM, block projected gradient descent, optimistic likelihood estimation, geodesically constrained subspace tracking, robust PCA, and Riemannian CP-dictionary-learning. We experimentally validate that our algorithm converges faster than standard Euclidean algorithms applied to the Riemannian setting.
Cubic-quartic regularization models for solving polynomial subproblems in third-order tensor methods
High-order tensor methods for solving both convex and nonconvex optimization problems have generated significant research interest, leading to algorithms with optimal global rates of convergence and local rates that are faster than Newton's method. On each iteration, these methods require the unconstrained local minimization of a (potentially nonconvex) multivariate polynomial of degree higher than two, constructed using third-order (or higher) derivative information, and regularized by an appropriate power of regularization. Developing efficient techniques for solving such subproblems is an ongoing topic of research, and this paper addresses the case of the third-order tensor subproblem. We propose the CQR algorithmic framework, for minimizing a nonconvex Cubic multivariate polynomial with Quartic Regularisation, by minimizing a sequence of local quadratic models that incorporate simple cubic and quartic terms. The role of the cubic term is to crudely approximate local tensor information, while the quartic one controls model regularization and progress. We provide necessary and sufficient optimality conditions that fully characterise the global minimizers of these cubic-quartic models. We then turn these conditions into secular equations that can be solved using nonlinear eigenvalue techniques. We show, using our optimality characterisations, that a CQR algorithmic variant has the optimal-order evaluation complexity of $\mathcal{O}(\epsilon^{-3/2})$ when applied to minimizing our quartically-regularised cubic subproblem, which can be further improved in special cases. We propose practical CQR variants that use local tensor information to construct the local cubic-quartic models. We test these variants numerically and observe them to be competitive with ARC and other subproblem solvers on typical instances and even superior on ill-conditioned subproblems with special structure.
The aim of this paper is to give a systematic mathematical interpretation of the diffusion problem on which Graph Neural Networks (GNNs) models are based. The starting point of our approach is a dissipative functional leading to dynamical equations which allows us to study the symmetries of the model. We discuss the conserved charges and provide a charge-preserving numerical method for solving the dynamical equations. In any dynamical system and also in GRAph Neural Diffusion (GRAND), knowing the charge values and their conservation along the evolution flow could provide a way to understand how GNNs and other networks work with their learning capabilities.
We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis testing is characterized by the Hellinger distance between the distributions. We show that the sample complexity of simple binary hypothesis testing under communication constraints is at most a logarithmic factor larger than in the unconstrained setting and this bound is tight. We develop a polynomial-time algorithm that achieves the aforementioned sample complexity. Our framework extends to robust hypothesis testing, where the distributions are corrupted in the total variation distance. Our proofs rely on a new reverse data processing inequality and a reverse Markov inequality, which may be of independent interest. For simple $M$-ary hypothesis testing, the sample complexity in the absence of communication constraints has a logarithmic dependence on $M$. We show that communication constraints can cause an exponential blow-up leading to $\Omega(M)$ sample complexity even for adaptive algorithms.
With the increasing demand of intelligent systems capable of operating in different contexts (e.g. users on the move) the correct interpretation of the user-need by such systems has become crucial to give consistent answers to the user questions. The most effective applications addressing such task are in the fields of natural language processing and semantic expansion of terms. These techniques are aimed at estimating the goal of an input query reformulating it as an intent, commonly relying on textual resources built exploiting different semantic relations like \emph{synonymy}, \emph{antonymy} and many others. The aim of this paper is to generate such resources using the labels of a given taxonomy as source of information. The obtained resources are integrated into a plain classifier for reformulating a set of input queries as intents and tracking the effect of each relation, in order to quantify the impact of each semantic relation on the classification. As an extension to this, the best tradeoff between improvement and noise introduction when combining such relations is evaluated. The assessment is made generating the resources and their combinations and using them for tuning the classifier which is used to reformulate the user questions as labels. The evaluation employs a wide and varied taxonomy as a use-case, exploiting its labels as basis for the semantic expansion and producing several corpora with the purpose of enhancing the pseudo-queries estimation.
Discovering underlying structures of causal relations from observational studies poses a great challenge in scientific research where randomized trials or intervention-based studies are infeasible. This challenge pertains to the lack of knowledge on pre-specified roles of cause and effect in observations studies. Leveraging Shannon's seminal work on information theory, we propose a new conceptual framework of asymmetry where any causal link between putative cause and effect is captured by unequal information flows from one variable to another. We present an entropy-based asymmetry coefficient that not only enables us to assess for whether one variable is a stronger predictor of the other, but also detects an imprint of the underlying causal relation in observational studies. Our causal discovery analytics can accommodate low-dimensional confounders naturally. The proposed methodology relies on scalable non-parametric density estimation using fast Fourier transformation, making the resulting estimation method manyfold faster than the classical bandwidth-based density estimation while maintaining comparable mean integrated squared error rates. We investigate key asymptotic properties of our methodology and utilize a data-splitting and cross-fitting technique to facilitate inference for the direction of causal relations. We illustrate the performance of our methodology through simulation studies and real data examples.
The prediction of chemical reactions has gained significant interest within the machine learning community in recent years, owing to its complexity and crucial applications in chemistry. However, model evaluation for this task has been mostly limited to simple metrics like top-k accuracy, which obfuscates fine details of a model's limitations. Inspired by progress in other fields, we propose a new assessment scheme that builds on top of current approaches, steering towards a more holistic evaluation. We introduce the following key components for this goal: CHORISO, a curated dataset along with multiple tailored splits to recreate chemically relevant scenarios, and a collection of metrics that provide a holistic view of a model's advantages and limitations. Application of this method to state-of-the-art models reveals important differences on sensitive fronts, especially stereoselectivity and chemical out-of-distribution generalization. Our work paves the way towards robust prediction models that can ultimately accelerate chemical discovery.
Robots cannot yet match humans' ability to rapidly learn the shapes of novel 3D objects and recognize them robustly despite clutter and occlusion. We present Bayes3D, an uncertainty-aware perception system for structured 3D scenes, that reports accurate posterior uncertainty over 3D object shape, pose, and scene composition in the presence of clutter and occlusion. Bayes3D delivers these capabilities via a novel hierarchical Bayesian model for 3D scenes and a GPU-accelerated coarse-to-fine sequential Monte Carlo algorithm. Quantitative experiments show that Bayes3D can learn 3D models of novel objects from just a handful of views, recognizing them more robustly and with orders of magnitude less training data than neural baselines, and tracking 3D objects faster than real time on a single GPU. We also demonstrate that Bayes3D learns complex 3D object models and accurately infers 3D scene composition when used on a Panda robot in a tabletop scenario.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191