Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact (log-)marginal likelihood. While VAEs are commonly used for representation learning, it is unclear why ELBO maximization would yield useful representations, since unregularized maximum likelihood estimation cannot invert the data-generating process. Yet, VAEs often succeed at this task. We seek to elucidate this apparent paradox by studying nonlinear VAEs in the limit of near-deterministic decoders. We first prove that, in this regime, the optimal encoder approximately inverts the decoder -- a commonly used but unproven conjecture -- which we refer to as {\em self-consistency}. Leveraging self-consistency, we show that the ELBO converges to a regularized log-likelihood. This allows VAEs to perform what has recently been termed independent mechanism analysis (IMA): it adds an inductive bias towards decoders with column-orthogonal Jacobians, which helps recovering the true latent factors. The gap between ELBO and log-likelihood is therefore welcome, since it bears unanticipated benefits for nonlinear representation learning. In experiments on synthetic and image data, we show that VAEs uncover the true latent factors when the data generating process satisfies the IMA assumption.
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Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.
Detecting and mitigating harmful biases in modern language models are widely recognized as crucial, open problems. In this paper, we take a step back and investigate how language models come to be biased in the first place. We use a relatively small language model, using the LSTM architecture trained on an English Wikipedia corpus. With full access to the data and to the model parameters as they change during every step while training, we can map in detail how the representation of gender develops, what patterns in the dataset drive this, and how the model's internal state relates to the bias in a downstream task (semantic textual similarity). We find that the representation of gender is dynamic and identify different phases during training. Furthermore, we show that gender information is represented increasingly locally in the input embeddings of the model and that, as a consequence, debiasing these can be effective in reducing the downstream bias. Monitoring the training dynamics, allows us to detect an asymmetry in how the female and male gender are represented in the input embeddings. This is important, as it may cause naive mitigation strategies to introduce new undesirable biases. We discuss the relevance of the findings for mitigation strategies more generally and the prospects of generalizing our methods to larger language models, the Transformer architecture, other languages and other undesirable biases.
The proliferation of automated data collection schemes and the advances in sensorics are increasing the amount of data we are able to monitor in real-time. However, given the high annotation costs and the time required by quality inspections, data is often available in an unlabeled form. This is fostering the use of active learning for the development of soft sensors and predictive models. In production, instead of performing random inspections to obtain product information, labels are collected by evaluating the information content of the unlabeled data. Several query strategy frameworks for regression have been proposed in the literature but most of the focus has been dedicated to the static pool-based scenario. In this work, we propose a new strategy for the stream-based scenario, where instances are sequentially offered to the learner, which must instantaneously decide whether to perform the quality check to obtain the label or discard the instance. The approach is inspired by the optimal experimental design theory and the iterative aspect of the decision-making process is tackled by setting a threshold on the informativeness of the unlabeled data points. The proposed approach is evaluated using numerical simulations and the Tennessee Eastman Process simulator. The results confirm that selecting the examples suggested by the proposed algorithm allows for a faster reduction in the prediction error.
As deep learning models have gradually become the main workhorse of time series forecasting, the potential vulnerability under adversarial attacks to forecasting and decision system accordingly has emerged as a main issue in recent years. Albeit such behaviors and defense mechanisms started to be investigated for the univariate time series forecasting, there are still few studies regarding the multivariate forecasting which is often preferred due to its capacity to encode correlations between different time series. In this work, we study and design adversarial attack on multivariate probabilistic forecasting models, taking into consideration attack budget constraints and the correlation architecture between multiple time series. Specifically, we investigate a sparse indirect attack that hurts the prediction of an item (time series) by only attacking the history of a small number of other items to save attacking cost. In order to combat these attacks, we also develop two defense strategies. First, we adopt randomized smoothing to multivariate time series scenario and verify its effectiveness via empirical experiments. Second, we leverage a sparse attacker to enable end-to-end adversarial training that delivers robust probabilistic forecasters. Extensive experiments on real dataset confirm that our attack schemes are powerful and our defend algorithms are more effective compared with other baseline defense mechanisms.
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized algorithms for spectral approximation, low-rank approximation/projection-cost preservation, and $\ell_1$-subspace embeddings in the sliding window model, which often use nearly optimal space and achieve nearly input sparsity runtime. Our algorithms are based on "reverse online" versions of offline sampling distributions such as (ridge) leverage scores, $\ell_1$ sensitivities, and Lewis weights to quantify both the importance and the recency of a row. Our row-sampling framework rather surprisingly implies connections to the well-studied online model; our structural results also give the first sample optimal (up to lower order terms) online algorithm for low-rank approximation/projection-cost preservation. Using this powerful primitive, we give online algorithms for column/row subset selection and principal component analysis that resolves the main open question of Bhaskara et. al.,(FOCS 2019). We also give the first online algorithm for $\ell_1$-subspace embeddings. We further formalize the connection between the online model and the sliding window model by introducing an additional unified framework for deterministic algorithms using a merge and reduce paradigm and the concept of online coresets. Our sampling based algorithms in the row-arrival online model yield online coresets, giving deterministic algorithms for spectral approximation, low-rank approximation/projection-cost preservation, and $\ell_1$-subspace embeddings in the sliding window model that use nearly optimal space.
GAN inversion aims to invert an input image into the latent space of a pre-trained GAN. Despite the recent advances in GAN inversion, there remain challenges to mitigate the tradeoff between distortion and editability, i.e. reconstructing the input image accurately and editing the inverted image with a small visual quality drop. The recently proposed pivotal tuning model makes significant progress towards reconstruction and editability, by using a two-step approach that first inverts the input image into a latent code, called pivot code, and then alters the generator so that the input image can be accurately mapped into the pivot code. Here, we show that both reconstruction and editability can be improved by a proper design of the pivot code. We present a simple yet effective method, named cycle encoding, for a high-quality pivot code. The key idea of our method is to progressively train an encoder in varying spaces according to a cycle scheme: W->W+->W. This training methodology preserves the properties of both W and W+ spaces, i.e. high editability of W and low distortion of W+. To further decrease the distortion, we also propose to refine the pivot code with an optimization-based method, where a regularization term is introduced to reduce the degradation in editability. Qualitative and quantitative comparisons to several state-of-the-art methods demonstrate the superiority of our approach.
Real-world databases are complex, they usually present redundancy and shared correlations between heterogeneous and multiple representations of the same data. Thus, exploiting and disentangling shared information between views is critical. For this purpose, recent studies often fuse all views into a shared nonlinear complex latent space but they lose the interpretability. To overcome this limitation, here we propose a novel method to combine multiple Variational AutoEncoders (VAE) architectures with a Factor Analysis latent space (FA-VAE). Concretely, we use a VAE to learn a private representation of each heterogeneous view in a continuous latent space. Then, we model the shared latent space by projecting every private variable to a low-dimensional latent space using a linear projection matrix. Thus, we create an interpretable hierarchical dependency between private and shared information. This way, the novel model is able to simultaneously: (i) learn from multiple heterogeneous views, (ii) obtain an interpretable hierarchical shared space, and, (iii) perform transfer learning between generative models.
Dynamic Time Warping is arguably the most popular similarity measure for time series, where we define a time series to be a one-dimensional polygonal curve. The drawback of Dynamic Time Warping is that it is sensitive to the sampling rate of the time series. The Fr\'echet distance is an alternative that has gained popularity, however, its drawback is that it is sensitive to outliers. Continuous Dynamic Time Warping (CDTW) is a recently proposed alternative that does not exhibit the aforementioned drawbacks. CDTW combines the continuous nature of the Fr\'echet distance with the summation of Dynamic Time Warping, resulting in a similarity measure that is robust to sampling rate and to outliers. In a recent experimental work of Brankovic et al., it was demonstrated that clustering under CDTW avoids the unwanted artifacts that appear when clustering under Dynamic Time Warping and under the Fr\'echet distance. Despite its advantages, the major shortcoming of CDTW is that there is no exact algorithm for computing CDTW, in polynomial time or otherwise. In this work, we present the first exact algorithm for computing CDTW of one-dimensional curves. Our algorithm runs in time $O(n^5)$ for a pair of one-dimensional curves, each with complexity at most $n$. In our algorithm, we propagate continuous functions in the dynamic program for CDTW, where the main difficulty lies in bounding the complexity of the functions. We believe that our result is an important first step towards CDTW becoming a practical similarity measure between curves.
In recent years, change point detection for high dimensional data has become increasingly important in many scientific fields. Most literature develop a variety of separate methods designed for specified models (e.g. mean shift model, vector auto-regressive model, graphical model). In this paper, we provide a unified framework for structural break detection which is suitable for a large class of models. Moreover, the proposed algorithm automatically achieves consistent parameter estimates during the change point detection process, without the need for refitting the model. Specifically, we introduce a three-step procedure. The first step utilizes the block segmentation strategy combined with a fused lasso based estimation criterion, leads to significant computational gains without compromising the statistical accuracy in identifying the number and location of the structural breaks. This procedure is further coupled with hard-thresholding and exhaustive search steps to consistently estimate the number and location of the break points. The strong guarantees are proved on both the number of estimated change points and the rates of convergence of their locations. The consistent estimates of model parameters are also provided. The numerical studies provide further support of the theory and validate its competitive performance for a wide range of models. The developed algorithm is implemented in the R package LinearDetect.
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.
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