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This paper proposes Fourier-based and wavelet-based techniques for analyzing periodic financial time series. Conventional models such as the periodic autoregressive conditional heteroscedastic (PGARCH) and periodic autoregressive…
Synthetic datasets are widely used in many applications, such as missing data imputation, examining non-stationary scenarios, in simulations, training data-driven models, and analyzing system robustness. Typically, synthetic data are based…
We propose a generative model that can infer a distribution for the underlying spatial signal conditioned on sparse samples e.g. plausible images given a few observed pixels. In contrast to sequential autoregressive generative models, our…
We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive…
Point processes offer a versatile framework for sequential event modeling. However, the computational challenges and constrained representational power of the existing point process models have impeded their potential for wider…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
The production of color language is essential for grounded language generation. Color descriptions have many challenging properties: they can be vague, compositionally complex, and denotationally rich. We present an effective approach to…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
We present a method for the generation of complex pulse sequences by using periodic spectral phase modulation. An analytical expression is derived for the temporal profile of such pulse sequences, which relates the temporal amplitudes and…
This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for…
This chapter presents an overview of techniques used for the analysis, edition, and synthesis of time series, with a particular emphasis on motion data. The use of mixture models allows the decomposition of time signals as a superposition…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
Recent progress in image generation has sparked research into controlling these models through condition signals, with various methods addressing specific challenges in conditional generation. Instead of proposing another specialized…
Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and…
Denoising diffusion models have gained popularity as a generative modeling technique for producing high-quality and diverse images. Applying these models to downstream tasks requires conditioning, which can take the form of text, class…
Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
The simulation of particle physics data is a fundamental but computationally intensive ingredient for physics analysis at the Large Hadron Collider, where observational set-valued data is generated conditional on a set of incoming…
Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…