In this work, we propose a generalization of the forward-forward (FF) algorithm that we call the predictive forward-forward (PFF) algorithm. Specifically, we design a dynamic, recurrent neural system that learns a directed generative circuit jointly and simultaneously with a representation circuit, combining elements of predictive coding, an emerging and viable neurobiological process theory of cortical function, with the forward-forward adaptation scheme. Furthermore, PFF efficiently learns to propagate learning signals and updates synapses with forward passes only, eliminating some of the key structural and computational constraints imposed by a backprop-based scheme. Besides computational advantages, the PFF process could be further useful for understanding the learning mechanisms behind biological neurons that make use of local (and global) signals despite missing feedback connections. We run several experiments on image data and demonstrate that the PFF procedure works as well as backprop, offering a promising brain-inspired algorithm for classifying, reconstructing, and synthesizing data patterns. As a result, our approach presents further evidence of the promise afforded by backprop-alternative credit assignment algorithms within the context of brain-inspired computing.
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The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently encountered in practice, the chain graph model has been largely under investigated in literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this paper, we first establish a set of novel identifiability conditions for the Gaussian chain graph model, exploiting a low rank plus sparse decomposition of the precision matrix. Further, an efficient learning algorithm is built upon the identifiability conditions to fully recover the chain graph structure. Theoretical analysis on the proposed method is conducted, assuring its asymptotic consistency in recovering the exact chain graph structure. The advantage of the proposed method is also supported by numerical experiments on both simulated examples and a real application on the Standard & Poor 500 index data.
Business process compliance is a key area of business process management and aims at ensuring that processes obey to compliance constraints such as regulatory constraints or business rules imposed on them. Process compliance can be checked during process design time based on verification of process models and at runtime based on monitoring the compliance states of running process instances. For existing compliance monitoring approaches it remains unclear whether and how compliance violations can be predicted, although predictions are crucial in order to prepare and take countermeasures in time. This work, hence, analyzes existing literature from compliance monitoring as well as predictive process monitoring and provides an updated framework of compliance monitoring functionalities. Moreover, it raises the vision of a comprehensive predictive compliance monitoring system that integrates existing predicate prediction approaches with the idea of employing PPM with different prediction goals such as next activity or remaining time for prediction and subsequent mapping of the prediction results onto the given set of compliance constraints (PCM). For each compliance monitoring functionality we elicit PCM system requirements and assess their coverage by existing approaches. Based on the assessment, open challenges and research directions realizing a comprehensive PCM system are elaborated.
We introduce a new algorithm and software for solving linear equations in symmetric diagonally dominant matrices with non-positive off-diagonal entries (SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate gradient (PCG) to solve the system of linear equations. Our preconditioner is a variant of the Approximate Cholesky factorization of Kyng and Sachdeva (FOCS 2016). Our factorization approach is simple: we eliminate matrix rows/columns one at a time and update the remaining matrix using sampling to approximate the outcome of complete Cholesky factorization. Unlike earlier approaches, our sampling always maintains a connectivity in the remaining non-zero structure. Our algorithm comes with a tuning parameter that upper bounds the number of samples made per original entry. We implement our algorithm in Julia, providing two versions, AC and AC2, that respectively use 1 and 2 samples per original entry. We compare their single-threaded performance to that of current state-of-the-art solvers Combinatorial Multigrid (CMG), BoomerAMG-preconditioned Krylov solvers from HyPre and PETSc, Lean Algebraic Multigrid (LAMG), and MATLAB's with Incomplete Cholesky Factorization (ICC). Our evaluation uses a broad class of problems, including all large SDDM matrices from the SuiteSparse collection and diverse programmatically generated instances. Our experiments suggest that our algorithm attains a level of robustness and reliability not seen before in SDDM solvers, while retaining good performance across all instances. Our code and data are public, and we provide a tutorial on how to replicate our tests. We hope that others will adopt this suite of tests as a benchmark, which we refer to as SDDM2023. Our solver code is available at: //github.com/danspielman/Laplacians.jl/ Our benchmarking data and tutorial are available at: //rjkyng.github.io/SDDM2023/
Single-shot auctions are commonly used as a means to sell goods, for example when selling ad space or allocating radio frequencies, however devising mechanisms for auctions with multiple bidders and multiple items can be complicated. It has been shown that neural networks can be used to approximate optimal mechanisms while satisfying the constraints that an auction be strategyproof and individually rational. We show that despite such auctions maximizing revenue, they do so at the cost of revealing private bidder information. While randomness is often used to build in privacy, in this context it comes with complications if done without care. Specifically, it can violate rationality and feasibility constraints, fundamentally change the incentive structure of the mechanism, and/or harm top-level metrics such as revenue and social welfare. We propose a method that employs stochasticity to improve privacy while meeting the requirements for auction mechanisms with only a modest sacrifice in revenue. We analyze the cost to the auction house that comes with introducing varying degrees of privacy in common auction settings. Our results show that despite current neural auctions' ability to approximate optimal mechanisms, the resulting vulnerability that comes with relying on neural networks must be accounted for.
In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially directed acyclic graph (PDAG), which contains both directed and undirected edges indicating uncertainty of causal relations between random variables. The main focus of this paper is on the maximal orientation task, which, for a given PDAG, aims to orient the undirected edges maximally such that the resulting graph represents the same Markov equivalent DAGs as the input PDAG. This task is a subroutine used frequently in causal discovery, e. g., as the final step of the celebrated PC algorithm. Utilizing connections to the problem of finding a consistent DAG extension of a PDAG, we derive faster algorithms for computing the maximal orientation by proposing two novel approaches for extending PDAGs, both constructed with an emphasis on simplicity and practical effectiveness.
Time series classification is an important problem in real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper, we propose to view the time series classification problem from the distribution perspective. We argue that the temporal complexity attributes to the unknown latent distributions within. To this end, we propose DIVERSIFY to learn generalized representations for time series classification. DIVERSIFY takes an iterative process: it first obtains the worst-case distribution scenario via adversarial training, then matches the distributions of the obtained sub-domains. We also present some theoretical insights. We conduct experiments on gesture recognition, speech commands recognition, wearable stress and affect detection, and sensor-based human activity recognition with a total of seven datasets in different settings. Results demonstrate that DIVERSIFY significantly outperforms other baselines and effectively characterizes the latent distributions by qualitative and quantitative analysis. Code is available at: //github.com/microsoft/robustlearn.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
Many natural language processing tasks solely rely on sparse dependencies between a few tokens in a sentence. Soft attention mechanisms show promising performance in modeling local/global dependencies by soft probabilities between every two tokens, but they are not effective and efficient when applied to long sentences. By contrast, hard attention mechanisms directly select a subset of tokens but are difficult and inefficient to train due to their combinatorial nature. In this paper, we integrate both soft and hard attention into one context fusion model, "reinforced self-attention (ReSA)", for the mutual benefit of each other. In ReSA, a hard attention trims a sequence for a soft self-attention to process, while the soft attention feeds reward signals back to facilitate the training of the hard one. For this purpose, we develop a novel hard attention called "reinforced sequence sampling (RSS)", selecting tokens in parallel and trained via policy gradient. Using two RSS modules, ReSA efficiently extracts the sparse dependencies between each pair of selected tokens. We finally propose an RNN/CNN-free sentence-encoding model, "reinforced self-attention network (ReSAN)", solely based on ReSA. It achieves state-of-the-art performance on both Stanford Natural Language Inference (SNLI) and Sentences Involving Compositional Knowledge (SICK) datasets.
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