Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its wide usage, understanding the theoretical properties of SVGD has remained a challenging problem. For sampling from a Gaussian target, the SVGD dynamics with a bilinear kernel will remain Gaussian as long as the initializer is Gaussian. Inspired by this fact, we undertake a detailed theoretical study of the Gaussian-SVGD, i.e., SVGD projected to the family of Gaussian distributions via the bilinear kernel, or equivalently Gaussian variational inference (GVI) with SVGD. We present a complete picture by considering both the mean-field PDE and discrete particle systems. When the target is strongly log-concave, the mean-field Gaussian-SVGD dynamics is proven to converge linearly to the Gaussian distribution closest to the target in KL divergence. In the finite-particle setting, there is both uniform in time convergence to the mean-field limit and linear convergence in time to the equilibrium if the target is Gaussian. In the general case, we propose a density-based and a particle-based implementation of the Gaussian-SVGD, and show that several recent algorithms for GVI, proposed from different perspectives, emerge as special cases of our unified framework. Interestingly, one of the new particle-based instance from this framework empirically outperforms existing approaches. Our results make concrete contributions towards obtaining a deeper understanding of both SVGD and GVI.
In this paper, we present a transformer architecture for predicting student performance on standardized tests. Specifically, we leverage students historical data, including their past test scores, study habits, and other relevant information, to create a personalized model for each student. We then use these models to predict their future performance on a given test. Applying this model to the RIIID dataset, we demonstrate that using multiple granularities for temporal features as the decoder input significantly improve model performance. Our results also show the effectiveness of our approach, with substantial improvements over the LightGBM method. Our work contributes to the growing field of AI in education, providing a scalable and accurate tool for predicting student outcomes.
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations, yielding theoretical estimates of learning rates which, unlike previous works, become increasingly tighter when the regularity of the unknown drift and diffusion coefficients becomes higher. Our method being kernel-based, offline pre-processing may in principle be profitably leveraged to enable efficient numerical implementation.
Recent data mining research has focused on the analysis of social media text, content and networks to identify suicide ideation online. However, there has been limited research on the temporal dynamics of users and suicide ideation. In this work, we use time-to-event modeling to identify which subreddits have a higher association with users transitioning to posting on r/suicidewatch. For this purpose we use a Cox proportional hazards model that takes as input text and subreddit network features and outputs a probability distribution for the time until a Reddit user posts on r/suicidewatch. In our analysis we find a number of statistically significant features that predict earlier transitions to r/suicidewatch. While some patterns match existing intuition, for example r/depression is positively associated with posting sooner on r/suicidewatch, others were more surprising (for example, the average time between a high risk post on r/Wishlist and a post on r/suicidewatch is 10.2 days). We then discuss these results as well as directions for future research.
Deterministic methods for motion planning guarantee safety amidst uncertainty in obstacle locations by trying to restrict the robot from operating in any possible location that an obstacle could be in. Unfortunately, this can result in overly conservative behavior. Chance-constrained optimization can be applied to improve the performance of motion planning algorithms by allowing for a user-specified amount of bounded constraint violation. However, state-of-the-art methods rely either on moment-based inequalities, which can be overly conservative, or make it difficult to satisfy assumptions about the class of probability distributions used to model uncertainty. To address these challenges, this work proposes a real-time, risk-aware reachability based motion planning framework called RADIUS. The method first generates a reachable set of parameterized trajectories for the robot offline. At run time, RADIUS computes a closed-form over-approximation of the risk of a collision with an obstacle. This is done without restricting the probability distribution used to model uncertainty to a simple class (e.g., Gaussian). Then, RADIUS performs real-time optimization to construct a trajectory that can be followed by the robot in a manner that is certified to have a risk of collision that is less than or equal to a user-specified threshold. The proposed algorithm is compared to several state-of-the-art chance-constrained and deterministic methods in simulation, and is shown to consistently outperform them in a variety of driving scenarios. A demonstration of the proposed framework on hardware is also provided.
Lexicon-based sentiment analysis (SA) in finance leverages specialized, manually annotated lexicons created by human experts to extract sentiment from financial texts. Although lexicon-based methods are simple to implement and fast to operate on textual data, they require considerable manual annotation efforts to create, maintain, and update the lexicons. These methods are also considered inferior to the deep learning-based approaches, such as transformer models, which have become dominant in various NLP tasks due to their remarkable performance. However, transformers require extensive data and computational resources for both training and testing. Additionally, they involve significant prediction times, making them unsuitable for real-time production environments or systems with limited processing capabilities. In this paper, we introduce a novel methodology named eXplainable Lexicons (XLex) that combines the advantages of both lexicon-based methods and transformer models. We propose an approach that utilizes transformers and SHapley Additive exPlanations (SHAP) for explainability to learn financial lexicons. Our study presents four main contributions. Firstly, we demonstrate that transformer-aided explainable lexicons can enhance the vocabulary coverage of the benchmark Loughran-McDonald (LM) lexicon, reducing the human involvement in annotating, maintaining, and updating the lexicons. Secondly, we show that the resulting lexicon outperforms the standard LM lexicon in SA of financial datasets. Thirdly, we illustrate that the lexicon-based approach is significantly more efficient in terms of model speed and size compared to transformers. Lastly, the XLex approach is inherently more interpretable than transformer models as lexicon models rely on predefined rules, allowing for better insights into the results of SA and making the XLex approach a viable tool for financial decision-making.
The algorithms used to train neural networks, like stochastic gradient descent (SGD), have close parallels to natural processes that navigate a high-dimensional parameter space -- for example protein folding or evolution. Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels in a single, unified framework. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium, exhibiting persistent currents in the space of network parameters. As in its physical analogues, the current is associated with an entropy production rate for any given training trajectory. The stationary distribution of these rates obeys the integral and detailed fluctuation theorems -- nonequilibrium generalizations of the second law of thermodynamics. We validate these relations in two numerical examples, a nonlinear regression network and MNIST digit classification. While the fluctuation theorems are universal, there are other aspects of the stationary state that are highly sensitive to the training details. Surprisingly, the effective loss landscape and diffusion matrix that determine the shape of the stationary distribution vary depending on the simple choice of minibatching done with or without replacement. We can take advantage of this nonequilibrium sensitivity to engineer an equilibrium stationary state for a particular application: sampling from a posterior distribution of network weights in Bayesian machine learning. We propose a new variation of stochastic gradient Langevin dynamics (SGLD) that harnesses without replacement minibatching. In an example system where the posterior is exactly known, this SGWORLD algorithm outperforms SGLD, converging to the posterior orders of magnitude faster as a function of the learning rate.
Cancelable biometrics are a group of techniques to transform the input biometric to an irreversible feature intentionally using a transformation function and usually a key in order to provide security and privacy in biometric recognition systems. This transformation is repeatable enabling subsequent biometric comparisons. This paper is introducing a new idea to exploit as a transformation function for cancelable biometrics aimed at protecting the templates against iterative optimization attacks. Our proposed scheme is based on time-varying keys (random biometrics in our case) and morphing transformations. An experimental implementation of the proposed scheme is given for face biometrics. The results confirm that the proposed approach is able to withstand against leakage attacks while improving the recognition performance.
We present a temporally layered architecture (TLA) for temporally adaptive control with minimal energy expenditure. The TLA layers a fast and a slow policy together to achieve temporal abstraction that allows each layer to focus on a different time scale. Our design draws on the energy-saving mechanism of the human brain, which executes actions at different timescales depending on the environment's demands. We demonstrate that beyond energy saving, TLA provides many additional advantages, including persistent exploration, fewer required decisions, reduced jerk, and increased action repetition. We evaluate our method on a suite of continuous control tasks and demonstrate the significant advantages of TLA over existing methods when measured over multiple important metrics. We also introduce a multi-objective score to qualitatively assess continuous control policies and demonstrate a significantly better score for TLA. Our training algorithm uses minimal communication between the slow and fast layers to train both policies simultaneously, making it viable for future applications in distributed control.
Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions. Most models for molecule generation rely on the decomposition of molecules into frequently occurring substructures (motifs), from which they generate novel compounds. While motif representations greatly aid in learning molecular distributions, such methods struggle to represent substructures beyond their known motif set. To alleviate this issue and increase flexibility across datasets, we propose MAGNet, a graph-based model that generates abstract shapes before allocating atom and bond types. To this end, we introduce a novel factorisation of the molecules' data distribution that accounts for the molecules' global context and facilitates learning adequate assignments of atoms and bonds onto shapes. While the abstraction to shapes introduces greater complexity for distribution learning, we show the competitive performance of MAGNet on standard benchmarks. Importantly, we demonstrate that MAGNet's improved expressivity leads to molecules with more topologically distinct structures and, at the same time, diverse atom and bond assignments.