We first provide sufficient conditions for the feasibility ofthe attackand an efficient algorithmtoperformanattack.

Battery health prognostics are critical for ensuring safety, efficiency, and sustainability in modern energy systems. However, it has been challenging to achieve accurate and robust prognostics due to complex battery degradation behaviors with nonlinearity, noise, capacity regeneration, etc. Existing data-driven models capture temporal degradation features but often lack knowledge guidance, which leads to unreliable long-term health prognostics. To overcome these limitations, we propose Karma, a knowledge-aware model with frequency-adaptive learning for battery capacity estimation and remaining useful life prediction. The model first performs signal decomposition to derive battery signals in different frequency bands. A dual-stream deep learning architecture is developed, where one stream captures long-term low-frequency degradation trends and the other models high-frequency short-term dynamics. Karma regulates the prognostics with knowledge, where battery degradation is modeled as a double exponential function based on empirical studies. Our dual-stream model is used to optimize the parameters of the knowledge with particle filters to ensure physically consistent and reliable prognostics and uncertainty quantification. Experimental study demonstrates Karma's superior performance, achieving average error reductions of 50.6% and 32.6% over state-of-the-art algorithms for battery health prediction on two mainstream datasets, respectively. These results highlight Karma's robustness, generalizability, and potential for safer and more reliable battery management across diverse applications.

Company fundamentals are key to assessing companies' financial and overall success and stability. Forecasting them is important in multiple fields, including investing and econometrics. While statistical and contemporary machine learning methods have been applied to many time series tasks, there is a lack of comparison of these approaches on this particularly challenging data regime. To this end, we try to bridge this gap and thoroughly evaluate the theoretical properties and practical performance of 22 deterministic and probabilistic company fundamentals forecasting models on real company data. We observe that deep learning models provide superior forcasting performance to classical models, in particular when considering uncertainty estimation. To validate the findings, we compare them to human analyst expectations and find that their accuracy is comparable to the automatic forecasts. We further show how these high-quality forecasts can benefit automated stock allocation. We close by presenting possible ways of integrating domain experts to further improve performance and increase reliability.

The Random Forest (RF) algorithm can be applied to a broad spectrum of problems, including time series prediction. However, neither the classical IID (Independent and Identically distributed) bootstrap nor block bootstrapping strategies (as implemented in rangerts) completely account for the nature of the Data Generating Process (DGP) while resampling the observations. We propose the combination of RF with a residual bootstrapping technique where we replace the IID bootstrap with the AR-Sieve Bootstrap (ARSB), which assumes the DGP to be an autoregressive process. To assess the new model's predictive performance, we conduct a simulation study using synthetic data generated from different types of DGPs. It turns out that ARSB provides more variation amongst the trees in the forest. Moreover, RF with ARSB shows greater accuracy compared to RF with other bootstrap strategies. However, these improvements are achieved at some efficiency costs.

This report provides an introduction to the ensmallen numerical optimization library, as well as a deep dive into the technical details of how it works. The library provides a fast and flexible C++ framework for mathematical optimization of arbitrary user-supplied functions. A large set of pre-built optimizers is provided, including many variants of Stochastic Gradient Descent and Quasi-Newton optimizers. Several types of objective functions are supported, including differentiable, separable, constrained, and categorical objective functions. Implementation of a new optimizer requires only one method, while a new objective function requires typically only one or two C++ methods. Through internal use of C++ template metaprogramming, ensmallen provides support for arbitrary user-supplied callbacks and automatic inference of unsupplied methods without any runtime overhead. Empirical comparisons show that ensmallen outperforms other optimization frameworks (such as Julia and SciPy), sometimes by large margins. The library is available at https://ensmallen.org and is distributed under the permissive BSD license.

We present an approach to clustering time series data using a model-based generalization of the K-Means algorithm which we call K-Models. We prove the convergence of this general algorithm and relate it to the hard-EM algorithm for mixture modeling. We then apply our method first with an AR($p$) clustering example and show how the clustering algorithm can be made robust to outliers using a least-absolute deviations criteria. We then build our clustering algorithm up for ARMA($p,q$) models and extend this to ARIMA($p,d,q$) models. We develop a goodness of fit statistic for the models fitted to clusters based on the Ljung-Box statistic. We perform experiments with simulated data to show how the algorithm can be used for outlier detection, detecting distributional drift, and discuss the impact of initialization method on empty clusters. We also perform experiments on real data which show that our method is competitive with other existing methods for similar time series clustering tasks.

It is worth noting that the observed data is uniquely orderly according to the time of observation, but it doesn't have to be dependent on time, i.e. time (index of the observations) doesn't have to be one of the independent variables. Stationarity: a stationary process is a stochastic process, whose mean, variance and autocorrelation structure do not change over time. It can also be defined formally using mathematical terms, but in this article, it's not necessary. Intuitively, if a time series is stationary, we look at some parts of them, they should be very similar -- the time series is flat looking and the shape doesn't depend on the shift of time. It surely isn't, since it's not stochastic, stationarity is not one of its properties) Figure 1.1 shows the simplest example of a stationary process -- white noise.

Learning the continuous equations of motion from discrete observations is a common task in all areas of physics. However, not any discretization of a Gaussian continuous-time stochastic process can be adopted in parametric inference. We show that discretizations yielding consistent estimators have the property of `invariance under coarse-graining', and correspond to fixed points of a renormalization group map on the space of autoregressive moving average (ARMA) models (for linear processes). This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order stochastic differential equations, even if the corresponding integration schemes may be acceptably good for numerical simulations.

We develop a new model of insulin-glucose dynamics for forecasting blood glucose in type 1 diabetics. We augment an existing biomedical model by introducing time-varying dynamics driven by a machine learning sequence model. Our model maintains a physiologically plausible inductive bias and clinically interpretable parameters -- e.g., insulin sensitivity -- while inheriting the flexibility of modern pattern recognition algorithms. Critical to modeling success are the flexible, but structured representations of subject variability with a sequence model. In contrast, less constrained models like the LSTM fail to provide reliable or physiologically plausible forecasts. We conduct an extensive empirical study. We show that allowing biomedical model dynamics to vary in time improves forecasting at long time horizons, up to six hours, and produces forecasts consistent with the physiological effects of insulin and carbohydrates.

Clustering time series is a delicate task; varying lengths and temporal offsets obscure direct comparisons. A natural strategy is to learn a parametric model foreach time series and to cluster the model parameters rather than the sequences themselves. Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical systems is a venerable task, permitting provably efficient solutions only in special cases. In this work, we show that clustering the parameters of unknown linear dynamical systems is, in fact, easier than identifying them. We analyze a computationally efficient clustering algorithm that enjoys provable convergence guarantees under a natural separation assumption. Although easy to implement, our algorithm is general, handling multi-dimensional data with time offsets and partial sequences. Evaluating our algorithm on both synthetic data and real electrocardiogram (ECG) signals, we see significant improvements in clustering quality over existing baselines.