Machine Learning Algorithms

Modeling something like time series goes past just throwing features in a model. In the world of time series data, each observation is associated with a specific time point, and part of our goal is to harness the power of temporal dependencies. Enter autoregression and lagging -  concepts that taps into the correlation between current and past observations to make forecasts.  At its core, autoregression involves modeling a time series as a function of its previous values. The current value relies on its historical counterparts. To dive a bit deeper, we use lagged values as features to predict the next data point. For instance, in a simple autoregressive model of order 1 (AR(1)), we predict the current value based on the previous value multiplied by a coefficient. The coefficient determines the impact of the past value on the present one only one time period previous. One popular approach that can be used in conjunction with autoregression is the ARIMA (AutoRegressive Integrated Moving Average) model. ARIMA is a powerful time series forecasting method that incorporates autoregression, differencing, and moving average components. It's particularly effective for data with trends and seasonality. ARIMA can be fine-tuned with parameters like the order of autoregression, differencing, and moving average to achieve accurate predictions. When I was building ARIMAs for econometric time series forecasting, in addition to autoregression where you're lagging the whole model, I was also taught to lag the individual economic variables. If I was building a model for energy consumption of residential homes, the number of housing permits each month would be a relevant variable. Although, if there’s a ton of housing permits given in January, you won’t see the actual effect of that until later when the houses are built and people are actually consuming energy! That variable needed to be lagged by several months. Another innovative strategy to enhance time series forecasting is the use of neural networks, particularly Recurrent Neural Networks (RNNs) or Long Short-Term Memory (LSTM) networks. RNNs and LSTMs are designed to handle sequential data like time series. They can learn complex patterns and long-term dependencies within the data, making them powerful tools for autoregressive forecasting. Neural networks are fed with past time steps as inputs to predict future values effectively. In addition to autoregression in neural networks, I also used lagging there too! When I built an hourly model to forecast electric energy consumption, I actually built 24 individual models, one for each hour, and each hour lagged on the previous one. The energy consumption and weather of the previous hour was very important in predicting what would happen in the next forecasting period. (this model was actually used for determining where they should shift electricity during peak load times). Happy forecasting!

🚨 Singapore published a case study applying its Agentic AI Framework (the world's first of its kind) to OpenClaw. [Download it below]. If you use AI agents, check out these SAFETY best practices: 1. Assess and bound the risks upfront - Avoid deploying OpenClaw in its open-source form in mission-critical environments - Avoid creating a single “all-powerful” OpenClaw agent with unrestricted access - Avoid installing OpenClaw on primary work or personal devices that contain sensitive data - Avoid granting OpenClaw ‘superuser’ privileges - Avoid granting OpenClaw unrestricted access to files and applications 2. Make humans meaningfully accountable - Adopt a risk-based approach to determine the appropriate level of agent autonomy with the sensitivity of data and the criticality of tasks - Identify checkpoints that require human approval - Enforce human approval through system-level controls where possible 3. Implement technical controls and processes a) During design and development - Enforce control-plane separation for key safety controls - Route outbound connections through a policy-enforcing proxy - Review and tighten the OpenClaw configurations, which are permissive by default - Avoid giving OpenClaw access to sensitive data - Use dedicated identities and credentials for the agent - Avoid exposing credentials to OpenClaw directly - Regularly rotate API keys, OAuth tokens, and other credentials used by the agent - Use trusted skills only - Use trusted sources b) Testing before deployment - Adopt a structured evaluation approach, organized around capability-based risk identification, concrete risk scenarios, as well as environment and tool mapping - Test and verify that safety controls are working as intended - Test and verify that human-in-the-loop (HITL) is working as intended - Test and verify that safeguards remain effective against indirect prompt injections, especially when third-party skills are used c) Post deployment - Ensure that all agent actions are logged and attributable - Avoid leaving the agent unsupervised for extended periods - Monitor the agent for behavioral anomalies and policy violations - Treat rebuild as an expected control, especially in the event of compromise or anomalous behavior - Regularly update OpenClaw and patch known vulnerabilities promptly 4.  Enable end-user responsibility - Provide personnel training and/or clear usage guidance - 👉 This is a super interesting case study, and a must-read for those developing or deploying AI agents. Download it below. 👉 To learn more and stay up to date, join my newsletter's 95,200+ subscribers (link below).

Shipping AI agents into production without governance is like deploying software without security, logs, or controls. It might work at first. But sooner or later, something breaks - silently. As AI agents move from experiments to real decision-makers, governance becomes infrastructure. This framework breaks AI Governance into the core functions every production-grade agent system needs: - Policy Rules Turn business and regulatory expectations into enforceable agent behavior - defining what agents can do, must avoid, and how they respond in restricted scenarios. - Access Control Limits agents to approved tools, datasets, and systems using identity verification, RBAC, and permission boundaries — preventing accidental or malicious misuse. - Audit Logs Create a full activity trail of agent decisions: what data was accessed, which tools were called, and why actions were taken — making every outcome traceable. - Risk Scoring Evaluates agent actions before execution, assigns risk levels, detects sensitive operations, and blocks unsafe decisions through thresholds and safety scoring. - Data Privacy Protects confidential information using PII detection, encryption, consent management, and retention policies — ensuring agents don’t leak regulated data. - Model Monitoring Tracks real-world agent performance: accuracy, drift, hallucinations, latency, and cost - keeping systems reliable after deployment. - Human Approvals Adds human-in-the-loop controls for high-impact actions, enabling escalation, overrides, and sign-offs when automation alone isn’t enough. - Incident Response Detects failures early and enables rapid containment through alerts, rollbacks, kill switches, and post-incident reporting to prevent repeat issues. The takeaway: AI agents don’t just need intelligence. They need guardrails. Without governance, agents become unpredictable. With governance, they become enterprise-ready. This is how organizations move from experimental AI to trustworthy, compliant, production systems. Save this if you’re building agentic systems. Share it with your platform or ML teams.

PCA (Principal Component Analysis) is a tricky concept to grasp. Here is a MATH-FREE explanation: Principal Component Analysis is a technique often used in Data Science & ML for "dimensionality reduction" This means it can help us reduce a large set of variables or features down to a smaller set that still contains much of the original information or variance! For example's sake, let's say our original dataset contained 10 numeric columns (features). PCA could reduce this set of ten features down to a smaller number of features (let's say 3) each of which is a "principal component" These newly created features or principal components are somewhat abstract. They are a blend of some of the original features, where the algorithm found they were correlated. By blending the original variables rather than simply removing them (like we might with feature selection techniques) we hope to keep much of the key information that is held within our original feature set. To be completely clear - in our example so far, the PCA algorithm itself did not choose to create 3, we, the Data Scientist actually pre-specified this number. Similar to algorithms like k-means, we have to tell the algorithm how many components we want to end up with - otherwise it will just construct a component for every original feature! So how do we decide how many components we want or need? There is no right or wrong answer to this question - we have a trade-off on our hands! We need to understand how much variance from the original feature set is captured by each additional principal component. Based on this, we must decide what is best for our task! [Pro Tips] Before applying PCA: Standardize your original features to ensure they all exist on a comparable scale Accept that you will lose some of the information/variance contained in your original data Accept that it may become more difficult to interpret the outputs of a model using components as inputs vs. the original features #datascience #analytics #data #datascienceinfinity

Factor Analysis vs. Principal Component Analysis Many people often confuse factor analysis (FA) and principal component analysis (PCA). While both are dimensionality reduction techniques, they serve different purposes. Principal Component Analysis (PCA) Principal Component Analysis is a technique that transforms the original variables into a new set of uncorrelated variables called principal components. These principal components are linear combinations of the original variables, and they are ordered in such a way that the first principal component explains the maximum possible variance in the data, the second principal component explains the next highest variance, and so on. The main goals of PCA are: 1. Variance Explanation: PCA aims to explain as much of the total variance in the dataset as possible. This is achieved by finding principal components that capture the maximum variance. 2. Dimensionality Reduction: By selecting a subset of the principal components, PCA reduces the dimensionality of the data while retaining most of the variability present in the original variables. 3. Orthogonality: Principal components are orthogonal to each other, ensuring that they capture distinct aspects of the data’s variance. Factor Analysis (FA) Factor Analysis is a statistical method used to identify latent variables, or factors, that explain the observed correlations among the original variables. These latent factors are not directly observed but are inferred from the patterns of covariance among the observed variables. The primary objectives of FA are: 1. Covariance Explanation: FA focuses on explaining the covariance among the original variables. It seeks to uncover underlying factors that account for the shared variance. 2. Latent Variables: The goal is to identify a smaller number of unobserved factors that can describe the relationships among the observed variables. These factors are assumed to be the source of the observed correlations. 3. Model-Based Approach: FA is based on a specific model where the observed variables are expressed as linear combinations of the factors plus unique error terms. Key Differences 1. Purpose: PCA aims to reduce dimensionality by explaining the total variance in the data, while FA seeks to uncover latent factors that explain the covariance among variables. 2. Components vs. Factors: PCA produces principal components that are linear combinations of the original variables and aim to capture as much variance as possible. FA identifies latent factors that are inferred from the observed variables and aims to explain the covariance structure. 3. Variance vs. Covariance: PCA focuses on maximizing variance explained by the components, whereas FA focuses on modeling the covariance structure of the data. In summary, while both PCA and FA are used for reducing the dimensionality of data, they serve different purposes and are based on different conceptual frameworks. #quant #regression #pca #factor #variance

Tax AI - A Tool or the Next Team Member? For decades, tax functions have been built around two constants: a. Interpreting ever-changing regulations b. Managing data and compliance with precision Now comes AI - not just automating, but reimagining how tax is delivered. a. A tool makes your job faster. b. A team member changes how you think, plan, and decide. Tax AI is moving beyond automation. Imagine a system that: a. Predicts risks before a tax officer raises a query b. Designs alternative structures for cross-border flows in seconds c. Learns from historic disputes and simulates outcomes d. Reads global policy shifts and tells you what they mean for tomorrow’s deal e. This isn’t science fiction - it’s the direction we’re heading. But here’s the real question: Are we, as tax leaders, ready to treat AI as a strategic colleague rather than a back-office tool? Because the future tax team may not just be humans using AI - it may be humans + AI, co-creating decisions. The role of the professional? Judgment, ethics, storytelling, and empathy. The role of AI? Scale, speed, and relentless accuracy. The winning tax function of tomorrow will know how to blend the two. So, when you picture your tax team five years from now - do you see AI sitting at that table? #Tax #AI #Leadership #FutureOfWork #TaxTechnology

𝗪𝗵𝗮𝘁 𝗶𝗳 𝘆𝗼𝘂 𝗰𝗼𝘂𝗹𝗱 𝗳𝗼𝗿𝗲𝗰𝗮𝘀𝘁 𝘁𝗵𝗲 𝗳𝘂𝘁𝘂𝗿𝗲 𝗯𝘆 𝘁𝗿𝗲𝗮𝘁𝗶𝗻𝗴 𝗻𝘂𝗺𝗯𝗲𝗿𝘀 𝗹𝗶𝗸𝗲 𝘄𝗼𝗿𝗱𝘀? That's exactly what Amazon did with Chronos. They took T5 (yes, the language model) and taught it to "read" time series data. The trick? Tokenize continuous values into ~4096 discrete bins. Suddenly, forecasting becomes next-token prediction. 𝗘𝘃𝗼𝗹𝘂𝘁𝗶𝗼𝗻: 📍 Chronos (Feb 2024) — Original release 📍 Chronos-Bolt (Nov 2024) — ~250× faster inference 📍 Chronos 2.0 (Oct 2025) — Multivariate support 𝗛𝗼𝘄 𝗶𝘁 𝘄𝗼𝗿𝗸𝘀: 🔹 𝘛5 𝘌𝘯𝘤𝘰𝘥𝘦𝘳-𝘋𝘦𝘤𝘰𝘥𝘦𝘳 — Bidirectional encoder captures dependencies; autoregressive decoder generates multi-step forecasts 🔹 𝘛𝘰𝘬𝘦𝘯𝘪𝘻𝘢𝘵𝘪𝘰𝘯 — Mean-scale values → quantize into bins → regression becomes classification. Now you can use all the LLM tricks. 🔹 𝘗𝘳𝘰𝘣𝘢𝘣𝘪𝘭𝘪𝘴𝘵𝘪𝘤 𝘖𝘶𝘵𝘱𝘶𝘵 — Outputs a distribution over bins per timestep. Sample → get prediction intervals with calibrated uncertainty. 🔹 𝘊𝘩𝘳𝘰𝘯𝘰𝘴-𝘉𝘰𝘭𝘵 — One-shot decoding (all future timesteps in one forward pass). ~250× speedup + ~5% accuracy gain via knowledge distillation. 𝗣𝗿𝗲𝘁𝗿𝗮𝗶𝗻𝗶𝗻𝗴: • Large corpus: energy, traffic, economics, weather, web traffic • Heavy augmentation: scaling, jittering, warping 𝗪𝗵𝘆 𝗶𝘁 𝗺𝗮𝘁𝘁𝗲𝗿𝘀: ✅ Bridges time series & NLP—use mature LLM infrastructure ✅ Native probabilistic forecasting ✅ Chronos 2.0: multivariate + cross-variable learning ✅ Multiple sizes (Mini → Large) ✅ Apache-2.0 license 𝗣𝗲𝗿𝘀𝗼𝗻𝗮𝗹 𝗻𝗼𝘁𝗲: Syama Sundar Rangapuram is one of the co-authors on this work. He taught me ML during my grad school days and helped me out more than I can say. Seeing his work shape the field like this — super proud. 🙌 The LLM playbook works for time series. Who knew? #TimeSeries #MachineLearning #Forecasting #AI #FoundationModels

Want to level up your forecasting skills: Check out Pythons NeuralProphet! Here is what you need to know about it: 𝗪𝗵𝗮𝘁 𝗶𝘀 𝗡𝗲𝘂𝗿𝗮𝗹𝗣𝗿𝗼𝗽𝗵𝗲𝘁? NeuralProphet is an open-source time series forecasting Python package that combines the simplicity and interpretability of Facebook’s Prophet package with the advanced capabilities of neural networks utilizing PyTorch. It is designed to handle complex patterns in your data, such as multiple seasonalities, trends, and holidays, while being easy to use and integrate into your existing workflows. 𝗠𝗮𝗶𝗻 𝗙𝗲𝗮𝘁𝘂𝗿𝗲𝘀: • 𝗡𝗲𝘂𝗿𝗮𝗹 𝗡𝗲𝘁𝘄𝗼𝗿𝗸 𝗜𝗻𝘁𝗲𝗴𝗿𝗮𝘁𝗶𝗼𝗻: Unlike traditional Prophet, NeuralProphet incorporates neural networks, which allow it to capture more patterns and dependencies in the data.    • 𝗙𝗹𝗲𝘅𝗶𝗯𝗶𝗹𝗶𝘁𝘆: It supports daily, weekly, monthly, and custom time frequencies, making it adaptable to various forecasting needs.    • 𝗖𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁-𝗕𝗮𝘀𝗲𝗱 𝗠𝗼𝗱𝗲𝗹: NeuralProphet models trends, seasonalities, and holidays as distinct components, making the forecasts more interpretable.    • 𝗔𝘂𝘁𝗼-𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝘃𝗲 𝗧𝗲𝗿𝗺𝘀: The inclusion of auto-regressive terms improves the model’s ability to predict future values based on past observations. 𝗪𝗵𝘆 𝗨𝘀𝗲 𝗡𝗲𝘂𝗿𝗮𝗹𝗣𝗿𝗼𝗽𝗵𝗲𝘁? 1. 𝗘𝗻𝗵𝗮𝗻𝗰𝗲𝗱 𝗔𝗰𝗰𝘂𝗿𝗮𝗰𝘆: By integrating neural networks, NeuralProphet can capture complex patterns and seasonality that traditional methods might miss. This leads to more accurate and reliable forecasts.     2. 𝗨𝘀𝗲𝗿-𝗙𝗿𝗶𝗲𝗻𝗱𝗹𝘆: NeuralProphet matches the simplicity of Prophet, making it accessible even if you’re not a deep learning expert. Its intuitive interface allows you to set up and run forecasts quickly.     3. 𝗜𝗻𝘁𝗲𝗿𝗽𝗿𝗲𝘁𝗮𝗯𝗶𝗹𝗶𝘁𝘆: Despite its advanced modeling capabilities, NeuralProphet maintains the interpretability of its components, helping you understand the underlying factors driving your forecasts.     4. 𝗙𝗹𝗲𝘅𝗶𝗯𝗶𝗹𝗶𝘁𝘆 𝗮𝗻𝗱 𝗖𝘂𝘀𝘁𝗼𝗺𝗶𝘇𝗮𝘁𝗶𝗼𝗻: Whether you’re dealing with daily sales data, monthly revenue, or weekly web traffic, NeuralProphet’s flexible framework can be tailored to meet your specific needs.     5. 𝗦𝗰𝗮𝗹𝗮𝗯𝗶𝗹𝗶𝘁𝘆: NeuralProphet can handle large datasets and multiple seasonalities, making it suitable for complex forecasting tasks in dynamic environments. Use the power of NeuralProphet to level up your forecasting game and deliver insights that drive business success. What tools are you using or plan to use for building forecasts? ---------------- ♻️ Share if you find this post useful ➕ Follow for more daily insights on how to grow your career in the data field #dataanlaytics #datascience #neuralprophet #python #forecasting

𝐖𝐡𝐚𝐭 𝐢𝐬 𝐒𝐢𝐧𝐠𝐮𝐥𝐚𝐫 𝐯𝐚𝐥𝐮𝐞 𝐝𝐞𝐜𝐨𝐦𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧 (𝐒𝐕𝐃)? Netflix has aproximatelly 300 million users and 15,000 movies. That's roughly 4.5 trillion possible user-movie combinations to search through. Comparing every user to every movie in real time? Impossibly slow. So instead of brute-forcing it, they use one technique from Linear algebra to learn compact representations of every user and every movie. It's called SVD and it is a powerful technique to factor any matrix into the product of 3 matrices, each with special properties. It reduces a matrix to its constituent parts in order to make certain subsequent matrix calculations simpler. 𝐇𝐨𝐰 𝐝𝐨𝐞𝐬 𝐢𝐭 𝐰𝐨𝐫𝐤? SVD decomposes that massive user-movie interaction matrix into 3 smaller matrices: M = U × Σ × Vᵀ SVD factorizes the original ratings matrix M into 3 matrices that work together: U (user matrix): each row represents one user as a vector in a 50-dimensional latent space. These 50 dimensions correspond to hidden patterns that SVD extracts from the data (like preference for action, tolerance for slow pacing, or affinity for specific directors). These are not predefined, SVD derives them from the structure of the ratings. Σ (singular value matrix) is a diagonal matrix containing 50 singular values, sorted from largest to smallest. Each value indicates how much its corresponding dimension contributes to the overall ratings. The first singular value captures the strongest pattern; the last captures the weakest. This is why truncation works: dropping the smallest values removes the dimensions that contribute the least. Vᵀ (movie matrix): each column of V (i.e., each row of Vᵀ) represents one movie as a vector in the same 50-dimensional latent space as the users. Because users and movies share the same space, their positions become directly comparable. To predict user i's rating for movie j, you compute: rating_ij = U_i · Σ · V_j Where U_i is the i-th row of U, Σ is the diagonal singular value matrix, and V_j is the j-th column of V (equivalently, the j-th row of Vᵀ transposed back). Predicting how much you'll like a movie becomes a simple matrix operation between your taste profile, the importance weights, and the movie's feature profile. 𝐖𝐡𝐲 𝐝𝐨𝐞𝐬 𝐭𝐡𝐢𝐬 𝐰𝐨𝐫𝐤? Because your preferences are predictable. If you watched Titanic and loved it, the recommendation system built on SVD will likely suggest The Notebook because it discovered the pattern from millions of users who behaved like you. This is what you should love about Linear algebra. You learn 1 concept, just 1, and suddenly you're seeing SVD inside Netflix, inside Google Images, inside Spotify, inside search engines. It's not hundreds of different algorithms. It's the same SVD, showing up everywhere. ♻️ If this helped SVD click for you, repost and send it to someone who's been avoiding Linear algebra. P.S. Link to my free newsletter in the comments 👇

Closing the sim-to-real gap in humanoid robotics requires massive simulation throughput and high-fidelity physics validation. WPP recently detailed their engineering pipeline, showing how they reduced reinforcement learning cycle times for complex humanoid locomotion from 24 hours down to less than 60 minutes. The hardware architecture relies on Google Cloud’s new G4 VMs (powered by NVIDIA RTX PRO 6000 Blackwell GPUs) running NVIDIA Isaac Sim, integrated closely with DeepMind’s MuJoCo physics engine. The mechanics: The team mapped raw human mocap data (over 200 degrees of freedom) down to a constrained 29-DOF OpenUSD digital twin. By leveraging a P2P GPU topology to bypass central processing bottlenecks, the infrastructure executed over 3 billion simulations in under an hour. The virtual environment continuously introduced physical micro-variances—simulated pushes, shifting floor friction, and momentum changes—to train the model against the chaos of the real world. The resulting reinforcement learning model was condensed into a highly efficient ONNX policy and deployed directly to the physical robot. This edge policy processes live IMU and joint telemetry to output immediate, stabilized motor commands. Reaching this scale of simulation volume is the precise engineering mechanism that allows control policies to handle unstructured physical deployment. To support the research, Unitree has open-sourced the underlying RL code on GitHub. Blog post : https://lnkd.in/g4-gWzTP #Robotics #PhysicalAI #ReinforcementLearning #MuJoCo #GoogleCloud #IsaacSim #Engineering