We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum likelihood estimation as an optimization problem: namely, as the minimization of a free energy functional. One way to solve this problem is to consider the discretization of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of the popular Stein variational gradient descent algorithm. In particular, we establish a descent lemma for this algorithm, which guarantees that the free energy decreases at each iteration. This method, and any other obtained as the discretization of the gradient flow, will necessarily depend on a learning rate which must be carefully tuned by the practitioner in order to ensure convergence at a suitable rate. With this in mind, we also propose another algorithm for optimizing the free energy which is entirely learning rate free, based on coin betting techniques from convex optimization. We validate the performance of our algorithms across a broad range of numerical experiments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning.
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This work focuses on the problem of hyper-parameter tuning (HPT) for robust (i.e., adversarially trained) models, shedding light on the new challenges and opportunities arising during the HPT process for robust models. To this end, we conduct an extensive experimental study based on 3 popular deep models, in which we explore exhaustively 9 (discretized) HPs, 2 fidelity dimensions, and 2 attack bounds, for a total of 19208 configurations (corresponding to 50 thousand GPU hours). Through this study, we show that the complexity of the HPT problem is further exacerbated in adversarial settings due to the need to independently tune the HPs used during standard and adversarial training: succeeding in doing so (i.e., adopting different HP settings in both phases) can lead to a reduction of up to 80% and 43% of the error for clean and adversarial inputs, respectively. On the other hand, we also identify new opportunities to reduce the cost of HPT for robust models. Specifically, we propose to leverage cheap adversarial training methods to obtain inexpensive, yet highly correlated, estimations of the quality achievable using state-of-the-art methods. We show that, by exploiting this novel idea in conjunction with a recent multi-fidelity optimizer (taKG), the efficiency of the HPT process can be enhanced by up to 2.1x.
We provide a rigorous analysis of training by variational inference (VI) of Bayesian neural networks in the two-layer and infinite-width case. We consider a regression problem with a regularized evidence lower bound (ELBO) which is decomposed into the expected log-likelihood of the data and the Kullback-Leibler (KL) divergence between the a priori distribution and the variational posterior. With an appropriate weighting of the KL, we prove a law of large numbers for three different training schemes: (i) the idealized case with exact estimation of a multiple Gaussian integral from the reparametrization trick, (ii) a minibatch scheme using Monte Carlo sampling, commonly known as Bayes by Backprop, and (iii) a new and computationally cheaper algorithm which we introduce as Minimal VI. An important result is that all methods converge to the same mean-field limit. Finally, we illustrate our results numerically and discuss the need for the derivation of a central limit theorem.
We revisit the binary adversarial wiretap channel (AWTC) of type II in which an active adversary can read a fraction $r$ and flip a fraction $p$ of codeword bits. The semantic-secrecy capacity of the AWTC II is partially known, where the best-known lower bound is non-constructive, proven via a random coding argument that uses a large number (that is exponential in blocklength $n$) of random bits to seed the random code. In this paper, we establish a new derandomization result in which we match the best-known lower bound of $1-H_2(p)-r$ where $H_2(\cdot)$ is the binary entropy function via a random code that uses a small seed of only $O(n^2)$ bits. Our random code construction is a novel application of pseudolinear codes -- a class of non-linear codes that have $k$-wise independent codewords when picked at random where $k$ is a design parameter. As the key technical tool in our analysis, we provide a soft-covering lemma in the flavor of Goldfeld, Cuff and Permuter (Trans. Inf. Theory 2016) that holds for random codes with $k$-wise independent codewords.
Federated learning methods enable model training across distributed data sources without data leaving their original locations and have gained increasing interest in various fields. However, existing approaches are limited, excluding many structured probabilistic models. We present a general and elegant solution based on structured variational inference, widely used in Bayesian machine learning, adapted for the federated setting. Additionally, we provide a communication-efficient variant analogous to the canonical FedAvg algorithm. The proposed algorithms' effectiveness is demonstrated, and their performance is compared with hierarchical Bayesian neural networks and topic models.
Variational quantum algorithms (VQAs) prevail to solve practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers. For variational quantum machine learning, a variational algorithm with model interpretability built into the algorithm is yet to be exploited. In this paper, we construct a quantum regression algorithm and identify the direct relation of variational parameters to learned regression coefficients, while employing a circuit that directly encodes the data in quantum amplitudes reflecting the structure of the classical data table. The algorithm is particularly suitable for well-connected qubits. With compressed encoding and digital-analog gate operation, the run time complexity is logarithmically more advantageous than that for digital 2-local gate native hardware with the number of data entries encoded, a decent improvement in noisy intermediate-scale quantum computers and a minor improvement for large-scale quantum computing Our suggested method of compressed binary encoding offers a remarkable reduction in the number of physical qubits needed when compared to the traditional one-hot-encoding technique with the same input data. The algorithm inherently performs linear regression but can also be used easily for nonlinear regression by building nonlinear features into the training data. In terms of measured cost function which distinguishes a good model from a poor one for model training, it will be effective only when the number of features is much less than the number of records for the encoded data structure to be observable. To echo this finding and mitigate hardware noise in practice, the ensemble model training from the quantum regression model learning with important feature selection from regularization is incorporated and illustrated numerically.
An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive algorithms in following scenarios: 1. In the stochastic optimization setting, we only receive stochastic gradients and the level of noise in evaluating them greatly affects the convergence rate. Tuning is typically required when without prior knowledge of the noise scale in order to achieve the optimal rate. Considering this, we designed and analyzed noise-adaptive algorithms that can automatically ensure (near)-optimal rates under different noise scales without knowing it. 2. In training deep neural networks, the scales of gradient magnitudes in each coordinate can scatter across a very wide range unless normalization techniques, like BatchNorm, are employed. In such situations, algorithms not addressing this problem of gradient scales can behave very poorly. To mitigate this, we formally established the advantage of scale-free algorithms that adapt to the gradient scales and presented its real benefits in empirical experiments. 3. Traditional analyses in non-convex optimization typically rely on the smoothness assumption. Yet, this condition does not capture the properties of some deep learning objective functions, including the ones involving Long Short-Term Memory networks and Transformers. Instead, they satisfy a much more relaxed condition, with potentially unbounded smoothness. Under this condition, we show that a generalized SignSGD algorithm can theoretically match the best-known convergence rates obtained by SGD with gradient clipping but does not need explicit clipping at all, and it can empirically match the performance of Adam and beat others. Moreover, it can also be made to automatically adapt to the unknown relaxed smoothness.
The time and effort involved in hand-designing deep neural networks is immense. This has prompted the development of Neural Architecture Search (NAS) techniques to automate this design. However, NAS algorithms tend to be slow and expensive; they need to train vast numbers of candidate networks to inform the search process. This could be alleviated if we could partially predict a network's trained accuracy from its initial state. In this work, we examine the overlap of activations between datapoints in untrained networks and motivate how this can give a measure which is usefully indicative of a network's trained performance. We incorporate this measure into a simple algorithm that allows us to search for powerful networks without any training in a matter of seconds on a single GPU, and verify its effectiveness on NAS-Bench-101, NAS-Bench-201, NATS-Bench, and Network Design Spaces. Our approach can be readily combined with more expensive search methods; we examine a simple adaptation of regularised evolutionary search. Code for reproducing our experiments is available at //github.com/BayesWatch/nas-without-training.
Sequential recommendation as an emerging topic has attracted increasing attention due to its important practical significance. Models based on deep learning and attention mechanism have achieved good performance in sequential recommendation. Recently, the generative models based on Variational Autoencoder (VAE) have shown the unique advantage in collaborative filtering. In particular, the sequential VAE model as a recurrent version of VAE can effectively capture temporal dependencies among items in user sequence and perform sequential recommendation. However, VAE-based models suffer from a common limitation that the representational ability of the obtained approximate posterior distribution is limited, resulting in lower quality of generated samples. This is especially true for generating sequences. To solve the above problem, in this work, we propose a novel method called Adversarial and Contrastive Variational Autoencoder (ACVAE) for sequential recommendation. Specifically, we first introduce the adversarial training for sequence generation under the Adversarial Variational Bayes (AVB) framework, which enables our model to generate high-quality latent variables. Then, we employ the contrastive loss. The latent variables will be able to learn more personalized and salient characteristics by minimizing the contrastive loss. Besides, when encoding the sequence, we apply a recurrent and convolutional structure to capture global and local relationships in the sequence. Finally, we conduct extensive experiments on four real-world datasets. The experimental results show that our proposed ACVAE model outperforms other state-of-the-art methods.
Graph Neural Networks (GNNs) for representation learning of graphs broadly follow a neighborhood aggregation framework, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs in capturing different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.
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