This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem whose solution corresponds to a distribution minimizing the difference between answers to the linear queries based on the true distribution and answers from a differentially private distribution. Against this background, we establish two new algorithms for corresponding differentially private data release: the first is based on the differentially private Frank-Wolfe method, the second combines randomized smoothing with stochastic convex optimization techniques for a solution to the saddle-point problem. While previous works assess the accuracy of differentially private algorithms with reference to the empirical data distribution, a key contribution of our work is a more natural evaluation of the proposed algorithms' accuracy with reference to the true data-generating distribution.
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A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with constant or diminishing learning rates, the proposed method can obtain a stationary point of the problem. Additionally, its rate of convergence with diminishing learning rates is verified to be superior to that of the conjugate gradient method. The proposed method is shown to minimize training loss functions faster than the existing adaptive methods in practical applications of image and text classification. Furthermore, in the training of generative adversarial networks, one version of the proposed method achieved the lowest Frechet inception distance score among those of the adaptive methods.
The ability of a robot to plan complex behaviors with real-time computation, rather than adhering to predesigned or offline-learned routines, alleviates the need for specialized algorithms or training for each problem instance. Monte Carlo Tree Search is a powerful planning algorithm that strategically explores simulated future possibilities, but it requires a discrete problem representation that is irreconcilable with the continuous dynamics of the physical world. We present Spectral Expansion Tree Search (SETS), a real-time, tree-based planner that uses the spectrum of the locally linearized system to construct a low-complexity and approximately equivalent discrete representation of the continuous world. We prove SETS converges to a bound of the globally optimal solution for continuous, deterministic and differentiable Markov Decision Processes, a broad class of problems that includes underactuated nonlinear dynamics, non-convex reward functions, and unstructured environments. We experimentally validate SETS on drone, spacecraft, and ground vehicle robots and one numerical experiment, each of which is not directly solvable with existing methods. We successfully show SETS automatically discovers a diverse set of optimal behaviors and motion trajectories in real time.
We propose a method for conducting algebraic program analysis (APA) incrementally in response to changes of the program under analysis. APA is a program analysis paradigm that consists of two distinct steps: computing a path expression that succinctly summarizes the set of program paths of interest, and interpreting the path expression using a properly-defined semantic algebra to obtain program properties of interest. In this context, the goal of an incremental algorithm is to reduce the analysis time by leveraging the intermediate results computed before the program changes. We have made two main contributions. First, we propose a data structure for efficiently representing path expression as a tree together with a tree-based interpreting method. Second, we propose techniques for efficiently updating the program properties in response to changes of the path expression. We have implemented our method and evaluated it on thirteen Java applications from the DaCapo benchmark suite. The experimental results show that both our method for incrementally computing path expression and our method for incrementally interpreting path expression are effective in speeding up the analysis. Compared to the baseline APA and two state-of-the-art APA methods, the speedup of our method ranges from 160X to 4761X depending on the types of program analyses performed.
Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.
We propose a novel formalism for describing Structural Causal Models (SCMs) as fixed-point problems on causally ordered variables, eliminating the need for Directed Acyclic Graphs (DAGs), and establish the weakest known conditions for their unique recovery given the topological ordering (TO). Based on this, we design a two-stage causal generative model that first infers in a zero-shot manner a valid TO from observations, and then learns the generative SCM on the ordered variables. To infer TOs, we propose to amortize the learning of TOs on synthetically generated datasets by sequentially predicting the leaves of graphs seen during training. To learn SCMs, we design a transformer-based architecture that exploits a new attention mechanism enabling the modeling of causal structures, and show that this parameterization is consistent with our formalism. Finally, we conduct an extensive evaluation of each method individually, and show that when combined, our model outperforms various baselines on generated out-of-distribution problems. The code is available on \href{//github.com/microsoft/causica/tree/main/research_experiments/fip}{Github}.
In this paper, we present an information-theoretic method for clustering mixed-type data, that is, data consisting of both continuous and categorical variables. The proposed approach is built on the deterministic variant of the Information Bottleneck algorithm, designed to optimally compress data while preserving its relevant structural information. We evaluate the performance of our method against four well-established clustering techniques for mixed-type data -- KAMILA, K-Prototypes, Factor Analysis for Mixed Data with K-Means, and Partitioning Around Medoids using Gower's dissimilarity -- using both simulated and real-world datasets. The results highlight that the proposed approach offers a competitive alternative to traditional clustering techniques, particularly under specific conditions where heterogeneity in data poses significant challenges.
Video summarization aims to eliminate visual redundancy while retaining key parts of video to construct concise and comprehensive synopses. Most existing methods use discriminative models to predict the importance scores of video frames. However, these methods are susceptible to annotation inconsistency caused by the inherent subjectivity of different annotators when annotating the same video. In this paper, we introduce a generative framework for video summarization that learns how to generate summaries from a probability distribution perspective, effectively reducing the interference of subjective annotation noise. Specifically, we propose a novel diffusion summarization method based on the Denoising Diffusion Probabilistic Model (DDPM), which learns the probability distribution of training data through noise prediction, and generates summaries by iterative denoising. Our method is more resistant to subjective annotation noise, and is less prone to overfitting the training data than discriminative methods, with strong generalization ability. Moreover, to facilitate training DDPM with limited data, we employ an unsupervised video summarization model to implement the earlier denoising process. Extensive experiments on various datasets (TVSum, SumMe, and FPVSum) demonstrate the effectiveness of our method.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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