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Register a new userMaximum Likelihood Estimation for Multimodal Learning with Missing Modality
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Added by
Fei Ma
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Multimodal learning has achieved great successes in many scenarios. Compared with unimodal learning, it can effectively combine the information from different modalities to improve the performance of learning tasks. In reality, the multimodal data may have missing modalities due to various reasons, such as sensor failure and data transmission error. In previous works, the information of the modality-missing data has not been well exploited. To address this problem, we propose an efficient approach based on maximum likelihood estimation to incorporate the knowledge in the modality-missing data. Specifically, we design a likelihood function to characterize the conditional distribution of the modality-complete data and the modality-missing data, which is theoretically optimal. Moreover, we develop a generalized form of the softmax function to effectively implement maximum likelihood estimation in an end-to-end manner. Such training strategy guarantees the computability of our algorithm capably. Finally, we conduct a series of experiments on real-world multimodal datasets. Our results demonstrate the effectiveness of the proposed approach, even when 95% of the training data has missing modality.
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A common assumption in multimodal learning is the completeness of training data, i.e., full modalities are available in all training examples. Although there exists research endeavor in developing novel methods to tackle the incompleteness of testing data, e.g., modalities are partially missing in testing examples, few of them can handle incomplete training modalities. The problem becomes even more challenging if considering the case of severely missing, e.g., 90% training examples may have incomplete modalities. For the first time in the literature, this paper formally studies multimodal learning with missing modality in terms of flexibility (missing modalities in training, testing, or both) and efficiency (most training data have incomplete modality). Technically, we propose a new method named SMIL that leverages Bayesian meta-learning in uniformly achieving both objectives. To validate our idea, we conduct a series of experiments on three popular benchmarks: MM-IMDb, CMU-MOSI, and avMNIST. The results prove the state-of-the-art performance of SMIL over existing methods and generative baselines including autoencoders and generative adversarial networks. Our code is available at https://github.com/mengmenm/SMIL.
The Reward-Biased Maximum Likelihood Estimate (RBMLE) for adaptive control of Markov chains was proposed to overcome the central obstacle of what is variously called the fundamental closed-identifiability problem of adaptive control, the dual control problem, or, contemporaneously, the exploration vs. exploitation problem. It exploited the key observation that since the maximum likelihood parameter estimator can asymptotically identify the closed-transition probabilities under a certainty equivalent approach, the limiting parameter estimates must necessarily have an optimal reward that is less than the optimal reward attainable for the true but unknown system. Hence it proposed a counteracting reverse bias in favor of parameters with larger optimal rewards, providing a solution to the fundamental problem alluded to above. It thereby proposed an optimistic approach of favoring parameters with larger optimal rewards, now known as optimism in the face of uncertainty. The RBMLE approach has been proved to be long-term average reward optimal in a variety of contexts. However, modern attention is focused on the much finer notion of regret, or finite-time performance. Recent analysis of RBMLE for multi-armed stochastic bandits and linear contextual bandits has shown that it not only has state-of-the-art regret, but it also exhibits empirical performance comparable to or better than the best current contenders, and leads to strikingly simple index policies. Motivated by this, we examine the finite-time performance of RBMLE for reinforcement learning tasks that involve the general problem of optimal control of unknown Markov Decision Processes. We show that it has a regret of $mathcal{O}( log T)$ over a time horizon of $T$ steps, similar to state-of-the-art algorithms. Simulation studies show that RBMLE outperforms other algorithms such as UCRL2 and Thompson Sampling.
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing observations. Using the Stochastic Block Model as a parametric proxy, we bound the risk of the maximum likelihood estimator of network connections probabilities , and show that it is minimax optimal. When risk is measured in Frobenius norm, no estimator running in polynomial time has been shown to attain the minimax optimal rate of convergence for this problem. Thus, maximum likelihood estimation is of particular interest as computationally efficient approximations to it have been proposed in the literature and are often used in practice.
The rising volume of datasets has made training machine learning (ML) models a major computational cost in the enterprise. Given the iterative nature of model and parameter tuning, many analysts use a small sample of their entire data during their initial stage of analysis to make quick decisions (e.g., what features or hyperparameters to use) and use the entire dataset only in later stages (i.e., when they have converged to a specific model). This sampling, however, is performed in an ad-hoc fashion. Most practitioners cannot precisely capture the effect of sampling on the quality of their model, and eventually on their decision-making process during the tuning phase. Moreover, without systematic support for sampling operators, many optimizations and reuse opportunities are lost. In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML training. BlinkML allows users to make error-computation tradeoffs: instead of training a model on their full data (i.e., full model), BlinkML can quickly train an approximate model with quality guarantees using a sample. The quality guarantees ensure that, with high probability, the approximate model makes the same predictions as the full model. BlinkML currently supports any ML model that relies on maximum likelihood estimation (MLE), which includes Generalized Linear Models (e.g., linear regression, logistic regression, max entropy classifier, Poisson regression) as well as PPCA (Probabilistic Principal Component Analysis). Our experiments show that BlinkML can speed up the training of large-scale ML tasks by 6.26x-629x while guaranteeing the same predictions, with 95% probability, as the full model.
Although deep learning models have driven state-of-the-art performance on a wide array of tasks, they are prone to learning spurious correlations that should not be learned as predictive clues. To mitigate this problem, we propose a causality-based training framework to reduce the spurious correlations caused by observable confounders. We give theoretical analysis on the underlying general Structural Causal Model (SCM) and propose to perform Maximum Likelihood Estimation (MLE) on the interventional distribution instead of the observational distribution, namely Counterfactual Maximum Likelihood Estimation (CMLE). As the interventional distribution, in general, is hidden from the observational data, we then derive two different upper bounds of the expected negative log-likelihood and propose two general algorithms, Implicit CMLE and Explicit CMLE, for causal predictions of deep learning models using observational data. We conduct experiments on two real-world tasks: Natural Language Inference (NLI) and Image Captioning. The results show that CMLE methods outperform the regular MLE method in terms of out-of-domain generalization performance and reducing spurious correlations, while maintaining comparable performance on the regular evaluations.
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