Given a user's risk preference and historical data, how can we generate diverse and high-quality portfolios for risk-aware portfolio optimization? Portfolio optimization is a core financial problem that balances returns and risks by determining asset allocations. While deterministic deep learning approaches can be directly optimized for a single solution, they offer limited flexibility to handle users' risk preferences. In contrast, stochastic methods typically rely on multi-stage processes, which complicate training and do not strictly align with the ultimate goal of generating optimal portfolios. In this paper, we propose Diffolio (Diffusion Models for Risk-Aware Portfolio Optimization), a novel diffusion-based framework that directly learns a pseudo-optimal portfolio distribution, addressing the drawbacks of (i) deterministic models lacking flexibility and (ii) stochastic models that are complex and misaligned with the true portfolio optimization objective. Instead of forecasting entire future time series, Diffolio directly samples portfolios, immediately adapting to user-specified risk levels through a dedicated risk guidance mechanism embedded in the denoising diffusion process. Empirical results on multiple real-world market datasets show that Diffolio significantly outperforms existing baselines in terms of return, risk control, and overall reliability. In particular, Diffolio achieves up to 12.1%p higher Annualized Rate of Return, demonstrating its strong potential as a risk-aware and objective-oriented solution to portfolio optimization.

How can we efficiently and accurately analyze an irregular tensor in a dual-way streaming setting where the sizes of two dimensions of the tensor increase over time? What types of anomalies are there in the dual-way streaming setting? An irregular tensor is a collection of matrices whose column lengths are the same while their row lengths are different. In a dual-way streaming setting, both new rows of existing matrices and new matrices arrive over time. PARAFAC2 decomposition is a crucial tool for analyzing irregular tensors. Although real-time analysis is necessary in the dual-way streaming, static PARAFAC2 decomposition methods fail to efficiently work in this setting since they perform PARAFAC2 decomposition for accumulated tensors whenever new data arrive. Existing streaming PARAFAC2 decomposition methods work in a limited setting and fail to handle new rows of matrices efficiently.

Given a temporal irregular tensor with missing values, how can we perform accurate decomposition for the tensor? Many real-world data can be represented as a temporal irregular tensor which is a collection of matrices whose rows corresponding to the time dimension have different sizes, but columns have the same size. PARAFAC2 decomposition is a powerful tool for analyzing an irregular tensor in many interesting applications such as phenotype discovery and fault detection. However, existing PARAFAC2 decomposition methods fail to handle irregular tensors with missing values since they treat the missing values as zeros. Furthermore, few methods that utilize temporal regularization focus only on a specific type of temporal irregular tensors.In this paper, we propose ATOM, an accurate PARAFAC2 decomposition method which carefully handles missing values in a temporal irregular tensor. ATOM provides a reformulated loss function that fully excludes missing values and accurately updates factor matrices by considering sparsity patterns of each row. ATOM also captures temporal patterns by exploiting smoothing regularization with time dependency. Extensive experiments show that ATOM provides up to 7.9× lower error rate than existing PARAFAC2 decomposition methods.