Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives.
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Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently, the algorithm offering the best tradeoff between compression rate, robustness, and speed for compressive sensing is the LASSO (l1-norm bias) algorithm. However, many studies have pointed out the possibility that the implementation of lp-norms biases, with p smaller than one, could give better performance while sacrificing convexity. In this work, we focus specifically on the extreme case of the l0-based reconstruction, a task that is complicated by the discontinuity of the loss. In the first part of the paper, we describe via statistical physics methods, and in particular the replica method, how the solutions to this optimization problem are arranged in a clustered structure. We observe two distinct regimes: one at low compression rate where the signal can be recovered exactly, and one at high compression rate where the signal cannot be recovered accurately. In the second part, we present two message-passing algorithms based on our first results for the l0-norm optimization problem. The proposed algorithms are able to recover the signal at compression rates higher than the ones achieved by LASSO while being computationally efficient.
Pulse timing is an important topic in nuclear instrumentation, with far-reaching applications from high energy physics to radiation imaging. While high-speed analog-to-digital converters become more and more developed and accessible, their potential uses and merits in nuclear detector signal processing are still uncertain, partially due to associated timing algorithms which are not fully understood and utilized. In this paper, we propose a novel method based on deep learning for timing analysis of modularized nuclear detectors without explicit needs of labelling event data. By taking advantage of the inner time correlation of individual detectors, a label-free loss function with a specially designed regularizer is formed to supervise the training of neural networks towards a meaningful and accurate mapping function. We mathematically demonstrate the existence of the optimal function desired by the method, and give a systematic algorithm for training and calibration of the model. The proposed method is validated on two experimental datasets. In the toy experiment, the neural network model achieves the single-channel time resolution of 8.8 ps and exhibits robustness against concept drift in the dataset. In the electromagnetic calorimeter experiment, several neural network models (FC, CNN and LSTM) are tested to show their conformance to the underlying physical constraint and to judge their performance against traditional methods. In total, the proposed method works well in either ideal or noisy experimental condition and recovers the time information from waveform samples successfully and precisely.
Processing-in-memory (PIM) promises to alleviate the data movement bottleneck in modern computing systems. However, current real-world PIM systems have the inherent disadvantage that their hardware is more constrained than in conventional processors (CPU, GPU), due to the difficulty and cost of building processing elements near or inside the memory. As a result, general-purpose PIM architectures support fairly limited instruction sets and struggle to execute complex operations such as transcendental functions and other hard-to-calculate operations (e.g., square root). These operations are particularly important for some modern workloads, e.g., activation functions in machine learning applications. In order to provide support for transcendental (and other hard-to-calculate) functions in general-purpose PIM systems, we present \emph{TransPimLib}, a library that provides CORDIC-based and LUT-based methods for trigonometric functions, hyperbolic functions, exponentiation, logarithm, square root, etc. We develop an implementation of TransPimLib for the UPMEM PIM architecture and perform a thorough evaluation of TransPimLib's methods in terms of performance and accuracy, using microbenchmarks and three full workloads (Blackscholes, Sigmoid, Softmax). We open-source all our code and datasets at~\url{//github.com/CMU-SAFARI/transpimlib}.
The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by large datasets for which the computation of the full gradient is prohibitively expensive. In this paper, we present two new variants of the FW algorithms for stochastic finite-sum minimization. Our algorithms have the best convergence guarantees of existing stochastic FW approaches for both convex and non-convex objective functions. Our methods do not have the issue of permanently collecting large batches, which is common to many stochastic projection-free approaches. Moreover, our second approach does not require either large batches or full deterministic gradients, which is a typical weakness of many techniques for finite-sum problems. The faster theoretical rates of our approaches are confirmed experimentally.
In dynamic interaction graphs, user-item interactions usually follow heterogeneous patterns, represented by different structural information, such as user-item co-occurrence, sequential information of user interactions and the transition probabilities of item pairs. However, the existing methods cannot simultaneously leverage all three structural information, resulting in suboptimal performance. To this end, we propose TriSIM4Rec, a triple structural information modeling method for accurate, explainable and interactive recommendation on dynamic interaction graphs. Specifically, TriSIM4Rec consists of 1) a dynamic ideal low-pass graph filter to dynamically mine co-occurrence information in user-item interactions, which is implemented by incremental singular value decomposition (SVD); 2) a parameter-free attention module to capture sequential information of user interactions effectively and efficiently; and 3) an item transition matrix to store the transition probabilities of item pairs. Then, we fuse the predictions from the triple structural information sources to obtain the final recommendation results. By analyzing the relationship between the SVD-based and the recently emerging graph signal processing (GSP)-based collaborative filtering methods, we find that the essence of SVD is an ideal low-pass graph filter, so that the interest vector space in TriSIM4Rec can be extended to achieve explainable and interactive recommendation, making it possible for users to actively break through the information cocoons. Experiments on six public datasets demonstrated the effectiveness of TriSIM4Rec in accuracy, explainability and interactivity.
This paper focuses on the information freshness of finite-state Markov sources, using the uncertainty of information (UoI) as the performance metric. Measured by Shannon's entropy, UoI can capture not only the transition dynamics of the Markov source but also the different evolutions of information quality caused by the different values of the last observation. We consider an information update system with M finite-state Markov sources transmitting information to a remote monitor via m communication channels. Our goal is to explore the optimal scheduling policy to minimize the sum-UoI of the Markov sources. The problem is formulated as a restless multi-armed bandit (RMAB). We relax the RMAB and then decouple the relaxed problem into M single bandit problems. Analyzing the single bandit problem provides useful properties with which the relaxed problem reduces to maximizing a concave and piecewise linear function, allowing us to develop a gradient method to solve the relaxed problem and obtain its optimal policy. By rounding up the optimal policy for the relaxed problem, we obtain an index policy for the original RMAB problem. Notably, the proposed index policy is universal in the sense that it applies to general RMABs with bounded cost functions.
This paper attempts to characterize the kinds of physical scenarios in which an online learning-based cognitive radar is expected to reliably outperform a fixed rule-based waveform selection strategy, as well as the converse. We seek general insights through an examination of two decision-making scenarios, namely dynamic spectrum access and multiple-target tracking. The radar scene is characterized by inducing a state-space model and examining the structure of its underlying Markov state transition matrix, in terms of entropy rate and diagonality. It is found that entropy rate is a strong predictor of online learning-based waveform selection, while diagonality is a better predictor of fixed rule-based waveform selection. We show that these measures can be used to predict first and second-order stochastic dominance relationships, which can allow system designers to make use of simple decision rules instead of more cumbersome learning approaches under certain conditions. We validate our findings through numerical results for each application and provide guidelines for future implementations.
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.
This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both the mixing coefficients and the community distribution are parameterized by the low-dimensional representations of the nodes and communities. We designed an effective variational inference algorithm which regularizes the community membership of neighboring nodes to be similar in the latent space. Experimental results on multiple real-world graphs show that vGraph is very effective in both community detection and node representation learning, outperforming many competitive baselines in both tasks. We show that the framework of vGraph is quite flexible and can be easily extended to detect hierarchical communities.
We propose a new method for event extraction (EE) task based on an imitation learning framework, specifically, inverse reinforcement learning (IRL) via generative adversarial network (GAN). The GAN estimates proper rewards according to the difference between the actions committed by the expert (or ground truth) and the agent among complicated states in the environment. EE task benefits from these dynamic rewards because instances and labels yield to various extents of difficulty and the gains are expected to be diverse -- e.g., an ambiguous but correctly detected trigger or argument should receive high gains -- while the traditional RL models usually neglect such differences and pay equal attention on all instances. Moreover, our experiments also demonstrate that the proposed framework outperforms state-of-the-art methods, without explicit feature engineering.
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