Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCausal learning with sufficient statistics: an information bottleneck approach
160
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional independencies between variables of a system are common tools for this purpose, but are limited in the lack of independencies. To surmount this limitation, we capitalize on the fact that the laws governing the generative mechanisms of a system often result in substructures embodied in the generative functional equation of a variable, which act as sufficient statistics for the influence that other variables have on it. These functional sufficient statistics constitute intermediate hidden variables providing new conditional independencies to be tested. We propose to use the Information Bottleneck method, a technique commonly applied for dimensionality reduction, to find underlying sufficient sets of statistics. Using these statistics we formulate new additional rules of causal orientation that provide causal information not obtainable from standard structure learning algorithms, which exploit only conditional independencies between observable variables. We validate the use of sufficient statistics for structure learning both with simulated systems built to contain specific sufficient statistics and with benchmark data from regulatory rules previously and independently proposed to model biological signal transduction networks.
rate research
Read More
In the standard data analysis framework, data is first collected (once for all), and then data analysis is carried out. With the advancement of digital technology, decisionmakers constantly analyze past data and generate new data through the decisions they make. In this paper, we model this as a Markov decision process and show that the dynamic interaction between data generation and data analysis leads to a new type of bias -- reinforcement bias -- that exacerbates the endogeneity problem in standard data analysis. We propose a class of instrument variable (IV)-based reinforcement learning (RL) algorithms to correct for the bias and establish their asymptotic properties by incorporating them into a two-timescale stochastic approximation framework. A key contribution of the paper is the development of new techniques that allow for the analysis of the algorithms in general settings where noises feature time-dependency. We use the techniques to derive sharper results on finite-time trajectory stability bounds: with a polynomial rate, the entire future trajectory of the iterates from the algorithm fall within a ball that is centered at the true parameter and is shrinking at a (different) polynomial rate. We also use the technique to provide formulas for inferences that are rarely done for RL algorithms. These formulas highlight how the strength of the IV and the degree of the noises time dependency affect the inference.
This paper investigates task-oriented communication for edge inference, where a low-end edge device transmits the extracted feature vector of a local data sample to a powerful edge server for processing. It is critical to encode the data into an informative and compact representation for low-latency inference given the limited bandwidth. We propose a learning-based communication scheme that jointly optimizes feature extraction, source coding, and channel coding in a task-oriented manner, i.e., targeting the downstream inference task rather than data reconstruction. Specifically, we leverage an information bottleneck (IB) framework to formalize a rate-distortion tradeoff between the informativeness of the encoded feature and the inference performance. As the IB optimization is computationally prohibitive for the high-dimensional data, we adopt a variational approximation, namely the variational information bottleneck (VIB), to build a tractable upper bound. To reduce the communication overhead, we leverage a sparsity-inducing distribution as the variational prior for the VIB framework to sparsify the encoded feature vector. Furthermore, considering dynamic channel conditions in practical communication systems, we propose a variable-length feature encoding scheme based on dynamic neural networks to adaptively adjust the activated dimensions of the encoded feature to different channel conditions. Extensive experiments evidence that the proposed task-oriented communication system achieves a better rate-distortion tradeoff than baseline methods and significantly reduces the feature transmission latency in dynamic channel conditions.
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in a hierarchy-preserving manner using a variety of metrics. Persistent homology is a tool commonly used in topological data analysis that is able to rigorously characterize a database in terms of both its hierarchy and connectivity structure. Computing persistent homology on a variety of embedded datasets reveals that some commonly used embeddings fail to preserve the connectivity. We show that those embeddings which successfully retain the database topology coincide in persistent homology by introducing two dilation-invariant comparative measures to capture this effect: in particular, they address the issue of metric distortion on manifolds. We provide an algorithm for their computation that exhibits greatly reduced time complexity over existing methods. We use these measures to perform the first instance of topology-based information retrieval and demonstrate its increased performance over the standard bottleneck distance for persistent homology. We showcase our approach on databases of different data varieties including text, videos, and medical images.
Decisions of complex language understanding models can be rationalized by limiting their inputs to a relevant subsequence of the original text. A rationale should be as concise as possible without significantly degrading task performance, but this balance can be difficult to achieve in practice. In this paper, we show that it is possible to better manage this trade-off by optimizing a bound on the Information Bottleneck (IB) objective. Our fully unsupervised approach jointly learns an explainer that predicts sparse binary masks over sentences, and an end-task predictor that considers only the extracted rationale. Using IB, we derive a learning objective that allows direct control of mask sparsity levels through a tunable sparse prior. Experiments on ERASER benchmark tasks demonstrate significant gains over norm-minimization techniques for both task performance and agreement with human rationales. Furthermore, we find that in the semi-supervised setting, a modest amount of gold rationales (25% of training examples) closes the gap with a model that uses the full input.
In many applications, it is desirable to extract only the relevant aspects of data. A principled way to do this is the information bottleneck (IB) method, where one seeks a code that maximizes information about a relevance variable, Y, while constraining the information encoded about the original data, X. Unfortunately however, the IB method is computationally demanding when data are high-dimensional and/or non-gaussian. Here we propose an approximate variational scheme for maximizing a lower bound on the IB objective, analogous to variational EM. Using this method, we derive an IB algorithm to recover features that are both relevant and sparse. Finally, we demonstrate how kerneliz
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
