Recent advances in machine learning-aided lossy compression are incorporating perceptual fidelity into the rate-distortion theory. In this paper, we study the rate-distortion-perception trade-off when the perceptual quality is measured by the total variation distance between the empirical and product distributions of the discrete memoryless source and its reconstruction. We consider the general setting, where two types of resources are available at both the encoder and decoder: a common side information sequence, correlated with the source sequence, and common randomness. We consider both the strong perceptual constraint and the weaker empirical perceptual constraint. The required communication rate for achieving the distortion and empirical perceptual constraint is the minimum conditional mutual information, and similar result holds for strong perceptual constraint when sufficient common randomness is provided and the output along with the side information is constraint to an independent and identically distributed sequence.
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For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the Euclidean or Manhattan distance). The Chamfer distance is a popular measure of dissimilarity between point clouds, used in many machine learning, computer vision, and graphics applications, and admits a straightforward $O(d n^2)$-time brute force algorithm. Further, the Chamfer distance is often used as a proxy for the more computationally demanding Earth-Mover (Optimal Transport) Distance. However, the \emph{quadratic} dependence on $n$ in the running time makes the naive approach intractable for large datasets. We overcome this bottleneck and present the first $(1+\epsilon)$-approximate algorithm for estimating the Chamfer distance with a near-linear running time. Specifically, our algorithm runs in time $O(nd \log (n)/\varepsilon^2)$ and is implementable. Our experiments demonstrate that it is both accurate and fast on large high-dimensional datasets. We believe that our algorithm will open new avenues for analyzing large high-dimensional point clouds. We also give evidence that if the goal is to \emph{report} a $(1+\varepsilon)$-approximate mapping from $A$ to $B$ (as opposed to just its value), then any sub-quadratic time algorithm is unlikely to exist.
Offline reinforcement learning (RL) offers an appealing approach to real-world tasks by learning policies from pre-collected datasets without interacting with the environment. However, the performance of existing offline RL algorithms heavily depends on the scale and state-action space coverage of datasets. Real-world data collection is often expensive and uncontrollable, leading to small and narrowly covered datasets and posing significant challenges for practical deployments of offline RL. In this paper, we provide a new insight that leveraging the fundamental symmetry of system dynamics can substantially enhance offline RL performance under small datasets. Specifically, we propose a Time-reversal symmetry (T-symmetry) enforced Dynamics Model (TDM), which establishes consistency between a pair of forward and reverse latent dynamics. TDM provides both well-behaved representations for small datasets and a new reliability measure for OOD samples based on compliance with the T-symmetry. These can be readily used to construct a new offline RL algorithm (TSRL) with less conservative policy constraints and a reliable latent space data augmentation procedure. Based on extensive experiments, we find TSRL achieves great performance on small benchmark datasets with as few as 1% of the original samples, which significantly outperforms the recent offline RL algorithms in terms of data efficiency and generalizability.
The triple-differences (TD) design is a popular identification strategy for causal effects in settings where researchers do not believe the parallel trends assumption of conventional difference-in-differences (DiD) is satisfied. TD designs augment the conventional 2x2 DiD with a "placebo" stratum -- observations that are nested in the same units and time periods but are known to be entirely unaffected by the treatment. However, many TD applications go beyond this simple 2x2x2 and use observations on many units in many "placebo" strata across multiple time periods. A popular estimator for this setting is the triple-differences regression (TDR) fixed-effects estimator -- an extension of the common "two-way fixed effects" estimator for DiD. This paper decomposes the TDR estimator into its component two-group/two-period/two-strata triple-differences and illustrates how interpreting this parameter causally in settings with arbitrary staggered adoption requires strong effect homogeneity assumptions as many placebo DiDs incorporate observations under treatment. The decomposition clarifies the implied identifying variation behind the triple-differences regression estimator and suggests researchers should be cautious when implementing these estimators in settings more complex than the 2x2x2 case. Alternative approaches that only incorporate "clean placebos" such as direct imputation of the counterfactual may be more appropriate. The paper concludes by demonstrating the utility of this imputation estimator in an application of the "gravity model" to the estimation of the effect of the WTO/GATT on international trade.
Advanced manipulation techniques have provided criminals with opportunities to make social panic or gain illicit profits through the generation of deceptive media, such as forged face images. In response, various deepfake detection methods have been proposed to assess image authenticity. Sequential deepfake detection, which is an extension of deepfake detection, aims to identify forged facial regions with the correct sequence for recovery. Nonetheless, due to the different combinations of spatial and sequential manipulations, forged face images exhibit substantial discrepancies that severely impact detection performance. Additionally, the recovery of forged images requires knowledge of the manipulation model to implement inverse transformations, which is difficult to ascertain as relevant techniques are often concealed by attackers. To address these issues, we propose Multi-Collaboration and Multi-Supervision Network (MMNet) that handles various spatial scales and sequential permutations in forged face images and achieve recovery without requiring knowledge of the corresponding manipulation method. Furthermore, existing evaluation metrics only consider detection accuracy at a single inferring step, without accounting for the matching degree with ground-truth under continuous multiple steps. To overcome this limitation, we propose a novel evaluation metric called Complete Sequence Matching (CSM), which considers the detection accuracy at multiple inferring steps, reflecting the ability to detect integrally forged sequences. Extensive experiments on several typical datasets demonstrate that MMNet achieves state-of-the-art detection performance and independent recovery performance.
Forward simulation-based uncertainty quantification that studies the distribution of quantities of interest (QoI) is a crucial component for computationally robust engineering design and prediction. There is a large body of literature devoted to accurately assessing statistics of QoIs, and in particular, multilevel or multifidelity approaches are known to be effective, leveraging cost-accuracy tradeoffs between a given ensemble of models. However, effective algorithms that can estimate the full distribution of QoIs are still under active development. In this paper, we introduce a general multifidelity framework for estimating the cumulative distribution function (CDF) of a vector-valued QoI associated with a high-fidelity model under a budget constraint. Given a family of appropriate control variates obtained from lower-fidelity surrogates, our framework involves identifying the most cost-effective model subset and then using it to build an approximate control variates estimator for the target CDF. We instantiate the framework by constructing a family of control variates using intermediate linear approximators and rigorously analyze the corresponding algorithm. Our analysis reveals that the resulting CDF estimator is uniformly consistent and asymptotically optimal as the budget tends to infinity, with only mild moment and regularity assumptions on the joint distribution of QoIs. The approach provides a robust multifidelity CDF estimator that is adaptive to the available budget, does not require \textit{a priori} knowledge of cross-model statistics or model hierarchy, and applies to multiple dimensions. We demonstrate the efficiency and robustness of the approach using test examples of parametric PDEs and stochastic differential equations including both academic instances and more challenging engineering problems.
We introduce a just-in-time runtime program transformation based on repeated recursion unfolding. Our online polyvariant program specialization generates several versions of a recursion differentiated by the minimal number of recursive steps covered. The base case of the recursion is ignored in our technique. Our method is presented here on the basis of linear direct recursive rules. When a recursive call is encountered at runtime, first an unfolder creates specializations of the associated recursive rule on-the-fly and then an interpreter applies these rules to the call. Our approach reduces the number of recursive rule applications to its logarithm at the expense of introducing a logarithmic number of unfolded rules. Each rule is applied at most once. We prove correctness of our technique and determine its worst-case time complexity. For recursions that solve tractable problems and which have enough unfoldings that can sufficiently simplified, we prove a super-linear speedup theorem, i.e. speedup by more than a constant factor. The simplification is problem-specific and has to be provided at compile-time. In the best case, the complexity of the given recursion is reduced to that of its first recursive step. We have implemented the necessary unfolder and meta-interpreter for runtime repeated recursion unfolding in Constraint Handling Rules (CHR) with just five rules. We illustrate the feasibility of our approach with complexity results and benchmarks for several classical algorithms. The runtime improvement quickly reaches several orders of magnitude.
Synthetic time series are often used in practical applications to augment the historical time series dataset for better performance of machine learning algorithms, amplify the occurrence of rare events, and also create counterfactual scenarios described by the time series. Distributional-similarity (which we refer to as realism) as well as the satisfaction of certain numerical constraints are common requirements in counterfactual time series scenario generation requests. For instance, the US Federal Reserve publishes synthetic market stress scenarios given by the constrained time series for financial institutions to assess their performance in hypothetical recessions. Existing approaches for generating constrained time series usually penalize training loss to enforce constraints, and reject non-conforming samples. However, these approaches would require re-training if we change constraints, and rejection sampling can be computationally expensive, or impractical for complex constraints. In this paper, we propose a novel set of methods to tackle the constrained time series generation problem and provide efficient sampling while ensuring the realism of generated time series. In particular, we frame the problem using a constrained optimization framework and then we propose a set of generative methods including ``GuidedDiffTime'', a guided diffusion model to generate realistic time series. Empirically, we evaluate our work on several datasets for financial and energy data, where incorporating constraints is critical. We show that our approaches outperform existing work both qualitatively and quantitatively. Most importantly, we show that our ``GuidedDiffTime'' model is the only solution where re-training is not necessary for new constraints, resulting in a significant carbon footprint reduction.
The accurate and efficient simulation of Partial Differential Equations (PDEs) in and around arbitrarily defined geometries is critical for many application domains. Immersed boundary methods (IBMs) alleviate the usually laborious and time-consuming process of creating body-fitted meshes around complex geometry models (described by CAD or other representations, e.g., STL, point clouds), especially when high levels of mesh adaptivity are required. In this work, we advance the field of IBM in the context of the recently developed Shifted Boundary Method (SBM). In the SBM, the location where boundary conditions are enforced is shifted from the actual boundary of the immersed object to a nearby surrogate boundary, and boundary conditions are corrected utilizing Taylor expansions. This approach allows choosing surrogate boundaries that conform to a Cartesian mesh without losing accuracy or stability. Our contributions in this work are as follows: (a) we show that the SBM numerical error can be greatly reduced by an optimal choice of the surrogate boundary, (b) we mathematically prove the optimal convergence of the SBM for this optimal choice of the surrogate boundary, (c) we deploy the SBM on massively parallel octree meshes, including algorithmic advances to handle incomplete octrees, and (d) we showcase the applicability of these approaches with a wide variety of simulations involving complex shapes, sharp corners, and different topologies. Specific emphasis is given to Poisson's equation and the linear elasticity equations.
Sufficient training data is normally required to train deeply learned models. However, the number of pedestrian images per ID in person re-identification (re-ID) datasets is usually limited, since manually annotations are required for multiple camera views. To produce more data for training deeply learned models, generative adversarial network (GAN) can be leveraged to generate samples for person re-ID. However, the samples generated by vanilla GAN usually do not have labels. So in this paper, we propose a virtual label called Multi-pseudo Regularized Label (MpRL) and assign it to the generated images. With MpRL, the generated samples will be used as supplementary of real training data to train a deep model in a semi-supervised learning fashion. Considering data bias between generated and real samples, MpRL utilizes different contributions from predefined training classes. The contribution-based virtual labels are automatically assigned to generated samples to reduce ambiguous prediction in training. Meanwhile, MpRL only relies on predefined training classes without using extra classes. Furthermore, to reduce over-fitting, a regularized manner is applied to MpRL to regularize the learning process. To verify the effectiveness of MpRL, two state-of-the-art convolutional neural networks (CNNs) are adopted in our experiments. Experiments demonstrate that by assigning MpRL to generated samples, we can further improve the person re-ID performance on three datasets i.e., Market-1501, DukeMTMCreID, and CUHK03. The proposed method obtains +6.29%, +6.30% and +5.58% improvements in rank-1 accuracy over a strong CNN baseline respectively, and outperforms the state-of-the- art methods.
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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