Mehmet Aktukmak

Mehmet Aktukmak, Daniel Huang, Ke Ding

Quantization is essential for reducing the computational cost and memory usage of deep neural networks, enabling efficient inference on low-precision hardware. Despite the growing adoption of uniform and floating-point quantization schemes, selecting optimal quantization parameters remains a key challenge, particularly for diverse data distributions encountered during training and inference. This work presents a novel statistical error analysis framework for uniform and floating-point quantization, providing theoretical insight into error behavior across quantization configurations. Building on this analysis, we propose iterative quantizers designed for arbitrary data distributions and analytic quantizers tailored for Gaussian-like weight distributions. These methods enable efficient, low-error quantization suitable for both activations and weights. We incorporate our quantizers into quantization-aware training and evaluate them across integer and floating-point formats. Experiments demonstrate improved accuracy and stability, highlighting the effectiveness of our approach for training low-precision neural networks.

Md Mahmuddun Nabi Murad, Mehmet Aktukmak, Yasin Yilmaz

Time series forecasting is crucial for various applications, such as weather forecasting, power load forecasting, and financial analysis. In recent studies, MLP-mixer models for time series forecasting have been shown as a promising alternative to transformer-based models. However, the performance of these models is still yet to reach its potential. In this paper, we propose Wavelet Patch Mixer (WPMixer), a novel MLP-based model, for long-term time series forecasting, which leverages the benefits of patching, multi-resolution wavelet decomposition, and mixing. Our model is based on three key components: (i) multi-resolution wavelet decomposition, (ii) patching and embedding, and (iii) MLP mixing. Multi-resolution wavelet decomposition efficiently extracts information in both the frequency and time domains. Patching allows the model to capture an extended history with a look-back window and enhances capturing local information while MLP mixing incorporates global information. Our model significantly outperforms state-of-the-art MLP-based and transformer-based models for long-term time series forecasting in a computationally efficient way, demonstrating its efficacy and potential for practical applications.

Yasin Yilmaz, Mehmet Aktukmak, Alfred O. Hero

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do not readily extend to heterogeneous data that are a combination of numerical and categorical variables, e.g., arising from linked GPS and text data. In this paper, we are interested in learning probabilistic generative models from high-dimensional heterogeneous data in an unsupervised fashion. The learned generative model provides latent unified representations that capture the factors common to the multiple dimensions of the data, and thus enable fusing multimodal data for various machine learning tasks. Following a Bayesian approach, we propose a general framework that combines disparate data types through the natural parameterization of the exponential family of distributions. To scale the model inference to millions of instances with thousands of features, we use the Laplace-Bernstein approximation for posterior computations involving nonlinear link functions. The proposed algorithm is presented in detail for the commonly encountered heterogeneous datasets with real-valued (Gaussian) and categorical (multinomial) features. Experiments on two high-dimensional and heterogeneous datasets (NYC Taxi and MovieLens-10M) demonstrate the scalability and competitive performance of the proposed algorithm on different machine learning tasks such as anomaly detection, data imputation, and recommender systems.