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2023: The Past, Present and Future of Chinese Economics
This article by Peking University Professor Yao Yang, calling for a greater focus on understanding Chinese domestic economic issues rather than theoretical issues reminds just slightly of the July 2023 article by Su Changhe, Dean of the School of International Relations and Public Affairs, Fudan University “China’s Autonomous Political Science Paradigm and Sharing it with the…
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#aging#China#Chinese economics#Communism#Communist Party#contributions#control#criticism#Daron Acemoglu#development#economics#entity list#financial accelerator#government procurement#Hai Wen#Hayek#Heckman#James Heckman#Joseph Stiglitz#market#market economy#Marx#Milton Friedman#planned economy#PRC#publish or perish#rule by law#rule of law#savings#Scott Rozelle
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oh chat..
#navigating losing my entire family amongst an accelerated curriculum which is Already baseline fast paced is so interesting /lh#in all seriousness i fear im slowly realizing the weight of how.. incredibly Unsustainable the relationship i have with my family is#esp given how ive been like literally.. slacking off on classes to the point of getting lower grades (mind u i think i ended off frshman yr#w a 3.96)#so..#trying to be kind and js move thru all moods with grace but chat it is Hard.#oh to deal with having no family while surrounded by people who do is so. like. disorienting#esp when ppl r like ‘yeah i wouldnt care if i was disowned’ but still say ily to their moms and cry over their parents like#chat i dont think ur being truly honest here.. and its not only unfair to you but it is to me ? bc like.. be so fr this is such a big. thing#looking into getting a depression diagnosis and Mayb meds tho so pray for me#currently struggling tho.. how does one communicate the loss of financial#familial#and cultural support#to their professors ??#blegh vent post bc im lowk losing my mind with how crazy everything is
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Why Quantum Computing Will Change the Tech Landscape
The technology industry has seen significant advancements over the past few decades, but nothing quite as transformative as quantum computing promises to be. Why Quantum Computing Will Change the Tech Landscape is not just a matter of speculation; it’s grounded in the science of how we compute and the immense potential of quantum mechanics to revolutionise various sectors. As traditional…
#AI#AI acceleration#AI development#autonomous vehicles#big data#classical computing#climate modelling#complex systems#computational power#computing power#cryptography#cybersecurity#data processing#data simulation#drug discovery#economic impact#emerging tech#energy efficiency#exponential computing#exponential growth#fast problem solving#financial services#Future Technology#government funding#hardware#Healthcare#industry applications#industry transformation#innovation#machine learning
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I am considering going back to school for a business degree :(
#gagged while typing that ew#i could get an associated in a year and I can do an accelerated course through my local community college#that would be entirely online + saturdays#I think it would help me at work + I miss school… and I could transfer to another college in town if I wanted a bachelors…#and I’m sure I could get financial aid bc the state paid for like half of my ba + the other scholarships I got… hrm#but idk if I want to tho. stewing on jt#ramblings
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Power Purchase Agreements Market Trends & Growth Analysis
#Market Overview :#The global Power Purchase Agreement (PPA) market is projected to grow from USD 36.6 billion in 2024 to approximately USD 604.2 billion by 2#expanding at a compound annual growth rate (CAGR) of 32.4% over the forecast period from 2025 to 2034.#The global Power Purchase Agreement (PPA) Market is undergoing a significant transformation#driven by the accelerated shift toward renewable energy and increasing demand for long-term#cost-effective energy procurement solutions. PPAs#which are contracts between energy producers and buyers for the sale of electricity over a fixed period#have emerged as a critical tool in enabling the decarbonization of the global energy sector. These agreements provide financial certainty f#making them highly attractive to both corporate entities and utilities.#The industrial scenario is marked by a surge in utility-scale solar and wind projects#often backed by long-term PPAs#particularly in regions like North America and Europe. Additionally#the Asia-Pacific region is witnessing increased adoption#driven by rapid industrialization and evolving regulatory landscapes. Innovations such as virtual PPAs (VPPAs)#aggregated PPAs#and shorter-term contracts are expanding the market's accessibility and flexibility#enabling small and medium enterprises (SMEs) to participate in renewable energy procurement.#Key Takeaways:#In 2024#the global power purchase agreement (PPA) market was valued at USD 36.6 billion.#The market is projected to grow at a compound annual growth rate (CAGR) of 32.4% between 2024 and 2034.#Virtual PPAs accounted for the largest market share by type#holding 59.9% in 2024.#Based on location#the off-site segment dominated the market with an 83.9% share in 2024.#By category#the corporate segment led the market#contributing 87.1% of the total share.#In terms of deal type#the wholesale segment held the highest share at 61.9% in 2024.
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Bloomberg AI Accelerates Financial Analysis with Rapid Targeted Insights
Bloomberg recently introduced AI-Powered Document Insights, a generative AI solution that enables financial analysts to quickly extract insights from complex business documents using natural language. Key Points: Improved Efficiency: Analysts can ask conversational questions to get precise answers from a wide range of business documents. Integration with Existing Tools: The solution integrates with other Bloomberg analytics tools, such as AI-Powered Earnings Call Summaries... read more: https://www.turtlesai.com/en/pages-2649/bloomberg-ai-accelerates-financial-analysis-with-rapid-targeted-insights
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AI and Business Strategy: The Secret to Sustainable, Scalable Success
AI and Business Strategy The Secret to Sustainable, Scalable Success Scaling is one thing. Sustaining it? That’s the real challenge. If you’ve been following this series, you know we’ve talked about AI-driven leadership, customer experience, and innovation—all crucial pieces of the puzzle. But today, we’re tackling something even more foundational: how AI transforms business strategy…
#AI-driven AI-enhanced executive workflows#AI-driven AI-first business frameworks#AI-driven AI-first executive decision-making#AI-driven AI-human hybrid strategy#AI-driven AI-powered workflow automation#AI-driven automated corporate vision execution#AI-driven business intelligence automation#AI-driven business model reinvention#AI-driven competitive intelligence#AI-driven cost optimization strategies#AI-driven cross-functional strategic execution#AI-driven customer behavior analysis#AI-driven data-backed competitive analysis#AI-driven digital transformation strategy#AI-driven executive decision support#AI-driven executive performance insights#AI-driven financial forecasting#AI-driven frictionless decision-making#AI-driven high-impact decision-making#AI-driven innovation acceleration#AI-driven intelligent automation for business success#AI-driven KPI tracking#AI-driven market intelligence tools#AI-driven next-gen business intelligence#AI-driven precision-driven corporate strategy#AI-driven predictive analytics#AI-driven real-time financial modeling#AI-driven risk assessment#AI-driven sales and marketing alignment#AI-driven smart decision automation
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The ongoing AI revolution is reshaping the world, one algorithm at a time - AI News
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The ongoing AI revolution is reshaping the world, one algorithm at a time - AI News
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In just a few years, the realm of AI has transcended its initial computational boundaries, emerging as one of the transformative forces of the 21st century, permeating virtually every major economic sector.
The global AI market was valued at $638.23 billion during Q4 2024, and is projected to reach a valuation of $3.6 trillion by 2034, largely because AI has the potential to gain widespread adoption in multiple industries.
For instance, in healthcare, 38% of all major medical providers use advanced AI diagnostic tools. Similarly, the financial sector has also demonstrated impressive integrations, with AI projected to contribute approx. $15.7 trillion to the global economy by 2030.
The retail industry has also set its sights on anywhere between $400 billion and $660 billion annually thanks to AI-driven customer experiences, while the cybersecurity sector is set to register a 23.6% growth rate – by 2027 – because of AI-powered intelligent security technologies.
It is estimated that about 83% of companies have already begun considering AI as a strategic priority, recognising its potential to drive innovation, enhance efficiency, and create competitive advantages.
Simplifying everyday life with AI
With the global tech landscape having transformed over the last couple of years, we are now at a point where AI is starting to automate various mundane and time-consuming everyday tasks.
The concept of ‘AI twins’ has gained traction recently, allowing individuals to manage scheduling, respond to emails, conduct research, and handle complex administrative tasks efficiently.
These digital companions represent more than just a caricature of a person’s real-world identity; they offer productivity accelerators designed to liberate anyone from repetitive work cycles (thus allowing them to focus on more creative, strategic, or emotionally nuanced tasks).
They can also help reduce the cognitive and emotional burden of managing multiple responsibilities, which could otherwise be overwhelming for some.
Leading this revolution is Twin Protocol, a platform that seeks to redefine how humans interact with AI, primarily via the creation of secure, dynamic digital representations that can learn, adapt, and evolve alongside their human counterparts.
By using the power of trained machine learning algorithms and decentralised ledgers, Twin Protocol allows individuals to develop digital twins that can capture not just information, but individual expertise and personality traits.
The platform’s potential spans industries, ranging from healthcare to manufacturing and finance. Imagine possessing the ability to deploy a perpetually-available AI twin that can provide personalised healthcare advice, or a digital representation of a financial advisor offering real-time, context-aware investment strategies.
These twins aren’t designed to serve as mere information repositories but as intelligent and dynamic tools capable of understanding context, learning continuously, and providing nuanced, personalised interactions.
What sets Twin Protocol apart is its commitment to maintaining individual agency and data privacy. Through its blockchain-based ‘Twin Vault‘, users can retain control over their digital identity, ensuring that personal information remains secure.
Thanks to its unique proposition, the platform has attracted several collaborations, including partnerships with SingularityNET and notable figures like Deepak Chopra and Robert Bell (founding member of Kool & the Gang).
AI’s potential is still uncharted
It is estimated that over the coming decade, AI’s potential could grow hugely, with offerings like Twin Protocol demonstrating next-generation technology, allowing users to explore new concepts like digital twins.
From personalised education to industrial optimisation, AI is moving beyond the category of being a tool, becoming a transformative partner capable of extending individual capabilities.
AI’s journey and symbiosis is likely to push the boundaries of what’s possible today. Some of the most exciting innovations emanating from the field will lie not in the technology, but in how its potential is applied to other fields. Interesting times are ahead!
#2024#accelerators#adoption#Advice#ai#ai news#AI-powered#algorithm#Algorithms#amp#Artificial Intelligence#author#billion#Blockchain#Capture#Companies#customer experiences#cybersecurity#data#data privacy#december#digital identity#digital twins#economic#economy#education#efficiency#emails#finance#financial
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Millionaire Partner System Member area and video courses
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The "Millionaire Partner System Member Area and Video Courses" is a game-changer for anyone looking to build a successful business partnership. The content is clear, actionable, and packed with valuable insights. The user-friendly member area makes navigation easy, while the video courses are high-quality and engaging. Each module is thoughtfully structured, offering step-by-step guidance that’s easy to follow. The additional tools, templates, and resources provided are incredibly helpful. It’s suitable for beginners and experienced entrepreneurs alike. With responsive customer support and regular updates, it truly delivers value for money. A must-try for those serious about achieving financial success!
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#The Millionaire Real Estate Investor: Strategies for Success in Property Investing#The Millionaire Real Estate Investor by Gary Keller is a comprehensive guide to achieving financial success through real estate investment.#providing practical advice#strategies#and case studies to empower readers to become successful investors. Keller begins the book by emphasizing the importance of mindset and at#focusing on the key principles of wealthy investors. By cultivating a mindset of abundance#opportunity#and continuous learning#readers can pave the way for financial success in real estate. The book then delves into the three main strategies for building wealth in#flipping#and renting. Keller explains each strategy in detail#outlining the benefits#risks#and key considerations for each approach. He provides practical tips on how to identify profitable investment opportunities#conduct market research#and navigate the complexities of real estate transactions. One of the key takeaways from The Millionaire Real Estate Investor is the conce#money#and expertise to maximize returns and scale investments. By building a network of professionals#partners#and advisors#readers can leverage resources to accelerate their real estate investment portfolio. Throughout the book#Keller shares real-life success stories and case studies of millionaire investors who have achieved financial freedom through real estate.#giving them a roadmap to follow and demonstrating that anyone can achieve success in real estate with the right mindset and strategies. In#The Millionaire Real Estate Investor also addresses the importance of financial planning and goal setting. Keller emphasizes the value of s#creating a financial plan#and tracking progress to achieve long-term success in real estate investment. Overall#The Millionaire Real Estate Investor is a must-read for anyone looking to build wealth through real estate. Whether you are a novice invest#the book offers valuable insights#practical advice#and actionable strategies to help you achieve financial success in real estate. I highly recommend The Millionaire Real Estate Investor to
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NVIDIA insights ahead of the AI Summit for Financial Services\
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Exciting AI Insights Ahead of Money20/20 Europe, the biggest event in Europe in Financial services. Get ahead with exclusive NVIDIA insights as we gear up for the AI Summit focused on Financial Services. Discover groundbreaking strategies, technological advancements, and industry trends poised to reshape finance. Dive into the latest AI applications, data analytics innovations, and the transformative potential of NVIDIA’s cutting-edge solutions. Stay ahead of the curve and unlock the power of AI in financial services with NVIDIA.
#nvidia ai#efi pylarinou#ai in financial services#artificial intelligence#accelerated computing platform#nvidia nimble#enhanced customer experience#improved risk management#data driven decision making#reduce cost of ai inference in finance with nvidia nimble#improve loan approval speed with nvidia dgx a100#the future of ai in apac financial services with nvidia#conversational ai for customer service#nvidia insights ahead of the ai#ai summit for financial services#Youtube
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The Driver Suit Blog-Paint Scheme Grades-May 18, 2024
By David G. Firestone Ross Chastain #1 Busch Light Throwback Chevy Camaro-Not a bad look, but the use of a more modern logo as opposed to the vintage Busch logo is a downgrade. C Austin Dillon #3 Bass Pro Shops/Tracker Off Road Throwback Chevy Camaro-YES! YES! YES! A THOUSAND TIMES YES! I love a good Dale Sr throwback, and this is a great Dale SR Throwback. A Josh Berry #4 Harrison’s Throwback…
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#Advent Health#alex bowman#Ally Financial#austin dillon#auto-owners insurance#Axalta#BallPark#bass pro shops#brad keselowski#busch light#camaro#Camry#castrol#Chase Briscoe#chevy#chevy camaro#Christopher Bell#corey lajoie#DeWalt#Dex Imaging#erik jones#Family Dollar#Focused Health#ford#ford mustang#Gener8tor Skills Accelerator#Harrison Burton#Harrison’s#Hendrickcars.com#John Hunter Nemechek
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Make 1K Every Day Fast And Simple Income Generating Proven Strategies for Success
To earn $1,000 every day, adopt proven income generating strategies that yield quick, significant returns. Seek out systems with a track record of financial success and user testimonials.
Making money quickly and consistently is a common goal for many, and reaching a target of $1,000 daily is an ambitious yet achievable objective. A multitude of online opportunities claim to offer the secret to financial prosperity, but discerning the legitimate from the too-good-to-be-true is crucial.
My Best Recommended & Proven Way to Make $100 Daily — Watch THIS FREE Training to START >>
Unlocking The Potential Of Daily Earnings
Unlocking the Potential of Daily Earnings is about turning each day into an opportunity. Imagine adding an extra $1,000 to your bank account daily. Such financial boosts can lead to a significant change in lifestyle and savings. Successful strategies exist. Follow them and you could see your income grow day by day.
Identifying High-profit Niches
Finding the right niche is critical for daily high-income potential. Look for industries with a huge demand but low competition. Do this by:
Researching market trends using tools like Google Trends.
Analyzing profitability through affiliate marketing platforms.
Spotting gaps in markets through customer reviews and forums.
Niches like health, wealth, and technology often promise better returns. Always ensure the niche aligns with your passion and expertise.
The Power Of Compound Earnings
Compound earnings can significantly increase your income over time. The key is to reinvest your earnings. See the power of compounding:
DayInitial Investment ($)Return Rate (%)Total Earnings ($)11,000101,100301,0001017,449
By consistently reinvesting your profits, small gains transform into large sums. Whether in stocks, savings accounts, or reinvestment in your business, compound earnings work.
Strategies That Deliver Results
Want to hit that 1K mark daily? Embrace strategies that work. Focus on tried-and-tested methods to generate income efficiently and effectively. The right strategies convert your efforts into steady earnings. Let’s dive into some powerful avenues for your financial breakthrough.
Leveraging Affiliate Marketing
Affiliate marketing offers a passive income stream. It’s simple: promote products and earn a commission for each sale. Start by choosing a niche you are passionate about. Next, find affiliate programs that fit your niche. These programs give you unique links to share. Share these links on your blog, social media, or email newsletters. When someone buys through your link, you get paid.
Join affiliate networks to find products to promote.
Understand your audience to offer relevant products.
Create high-quality content that adds value and includes your affiliate links.
Creating Digital Products
Digital products have high margins and unlimited potential. Think of ebooks, online courses, and software. They require upfront work but can earn money repeatedly without additional costs. Identify what you’re good at. Develop a product that solves problems or provides knowledge. Market your products online using social media, your website, and other platforms.
Type of Digital ProductDescriptionPotential IncomeEbooksWrite and sell your expertise.HighOnline CoursesTeach skills you’ve mastered.Very HighSoftwareCreate tools that help others.Scalable
Offering Freelance Services
Freelancing lets you capitalize on your skills. Millions outsource tasks and projects daily. Platforms like Upwork, Freelancer, and Fiverr connect freelancers with clients. Whether it’s writing, graphic design, or web development, you can offer services worldwide. Set competitive rates. Deliver top-notch work. Build a strong profile. Sustain a client base that trusts your expertise.
Set up profiles on freelancing platforms highlighting your skills.
Build a portfolio showcasing your best work.
Network to nurture client relationships and get repeat business.
My Best Recommended & Proven Way to Make $100 Daily — Watch THIS FREE Training to START >>
Strengthen Your Online Presence
Want to pocket an extra 1K daily? A powerful online presence is your secret weapon. Dive into strategies that catapult your success. Let’s explore!
Building A Persuasive Social Media Profile
Start with a smart profile picture. It’s your digital handshake. A professional headshot builds trust.
Write a bio that pops. In just a few words, tell your story. Make every word count.
Highlight your skills, what makes you unique.
Update regularly. Keep your achievements fresh.
Engage them. Post content they love. Respond to comments. Keep the conversation lively.
Effective Blogging Techniques
Create compelling headlines. Make them curious. They’ll want to read more.
Know your audience. Write what speaks to them. Solve their problems.
Use short paragraphs. Make it easy to read.
Include images. A picture says a thousand words.
Optimize with keywords. Get found on search engines. But keep it natural.
Call to action. Tell them what to do next. And make it stand out.
Maximizing Passive Income Streams
Earning $1K every day can seem like a dream, but it’s doable with passive income. Passive income streams require upfront effort or investment, but can pay off continuously. They are a key strategy for steady earnings without day-to-day work. Let’s explore some proven methods.
Investing In Dividend Stocks
One powerful revenue source is dividend stocks. Companies pay you just for holding their stock. Here’s how to get started:
Choose established, reliable companies.
Invest in diversified industries for safety.
Reinvest dividends for compounding interest.
Over time, the right portfolio might generate substantial daily income.
For clarity, here’s a simple comparison:
Stock TypeFrequency of PayPotential ReturnsHigh-yieldQuarterlyHigher risk, higher returnsBlue-chipAnnualStable, lower returns
Real Estate Income Opportunities
Real estate is another great way to earn passively. You can earn in two main ways:
Rental properties provide regular monthly income.
Real estate investment trusts (REITs) offer stock-like ease with dividends.
Both ways can help in hitting that $1K daily goal.
Here’s a snapshot of real estate income potential:
Property TypeExpected IncomeProperty ManagementSingle-family homeDepends on locationPossible self-managementMulti-family complexHigher potentialOften requires a manager
My Best Recommended & Proven Way to Make $100 Daily — Watch THIS FREE Training to START >>
Automation And Scaling Up
Embracing the power of automation and scaling your businesses can transform the quest for making 1K every day from a dream into reality. It’s about working smarter, not harder. Leverage these strategies to multiply your revenue streams efficiently.
Incorporating Automation Tools
Time is money, and automation tools save you both. Automate mundane tasks. Discover tools that align with your business goals.
Email marketing software crafts and sends emails while you sleep.
Social media management platforms queue posts for optimal engagement.
Use accounting software for instant invoicing and expense tracking.
Simple integrations bring big impacts on efficiency. Select tools offering comprehensive analytics. This helps you understand what works for your audience.
Expanding Your Income Channels
Expand beyond one revenue stream. Diversify. More channels mean more opportunities to earn.
Start an e-commerce store. Sell goods related to your brand.
Create an online course. Share your expertise.
Explore affiliate marketing. Recommend products and earn commissions.
Each channel should fit your overall strategy. They must also resonate with your target audience. Observe market trends. Adapt and scale these channels as needed.
ChannelPotential EarningsEase of ScalingE-commerceHighMediumOnline CoursesVariesHighAffiliate MarketingLow to HighHigh
Review the performance of each channel. Reinvest profits for further growth. Success in scaling means careful planning and execution.
Adapting For Consistency And Growth
The journey to making 1K every day is an exciting challenge. The key to success lies in adapting for consistency and growth. You must navigate through changes and keep up the momentum. Let’s dive into strategies that can help you stay ahead of the game.
Adaptability In Market Trends
Staying ahead means knowing the market. Adaptability is about making quick changes. Here’s how:
Research — Keep an eye on market shifts.
Learn — Embrace new skills that the market demands.
Innovate — Try different methods to stand out.
Flexibility helps you use new trends to your advantage. It turns challenges into opportunities. Change is constant, and your strategy should be too.
Maintaining Growth Momentum
Growth is essential. Here’s how to maintain the momentum:
StrategyActionSet GoalsHave clear, measurable targets.Analyze DataReview your progress regularly.OptimizeAdjust strategies based on performance.
By setting goals and analyzing data, you make informed decisions. Optimization ensures your tactics stay effective. A strong foundation leads to sustainable earnings.
Frequently Asked Questions
Q. Can I Make $1000 Daily Online?
Yes, with the right strategies, such as affiliate marketing, freelancing, or e-commerce, earning $1000 daily is possible online.
Q. What Are Fast Income-generating Methods?
Quick income can be made through high-commission affiliate programs, dropshipping, or offering in-demand digital services like web design.
Q. Is Passive Income Achievable Quickly?
Building passive income streams like dividend stocks or rental properties typically takes time, but some digital products can yield faster results.
Q. Are There Proven Strategies To Make Money?
Absolutely, proven money-making strategies include investing in stocks, starting a blog with monetizable content, and creating online courses.
Q. How To Start Earning $1k From Home?
To earn $1K from home, look into remote jobs, begin freelance writing or graphic design, or set up a home-based business online.
Conclusion
Embracing these strategies can unlock the door to consistent financial growth. Forget long hours and complex methods; here’s a path to a simpler yet effective income boost. Start your journey towards earning $1k daily — your potential awaits. Take action, refine your approach, and watch success unfold.
Let’s make prosperity your new normal.
My Best Recommended & Proven Way to Make $100 Daily — Watch THIS FREE Training to START >>
Thanks for reading my article on How I Increase My New Website from 0 to 1000 of Daily Visitors Step-By-Step Guide
Affiliate Disclaimer :
This article Contain may be affiliate links, which means I receive a small commission at NO ADDITIONAL cost to you if you decide to purchase something. While we receive affiliate compensation for reviews / promotions on this article, we always offer honest opinions, users experiences and real views related to the product or service itself. Our goal is to help readers make the best purchasing decisions, however, the testimonies and opinions expressed are ours only. As always you should do your own thoughts to verify any claims, results and stats before making any kind of purchase. Clicking links or purchasing products recommended in this article may generate income for this product from affiliate commissions and you should assume we are compensated for any purchases you make. We review products and services you might find interesting. If you purchase them, we might get a share of the commission from the sale from our partners. This does not drive our decision as to whether or not a product is featured or recommended.
Source : Make 1K Every Day Fast And Simple Income Generating Proven Strategies for Success
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Unlocking Financial Success: The Power of Multiple Streams of Income
Written by Delvin In today’s fast-paced world, achieving financial success is a goal that many strive for. While there are various paths to wealth accumulation, one intriguing concept stands out: the average millionaire has seven streams of income. This fun fact underscores the importance of diversifying income sources and highlights the potential benefits it can bring. In this blog post, we…
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#Accelerated Wealth Creation#dailyprompt#Developing Financial Independence#Diversification#Financial#Financial Freedom#Financial Literacy#Generational Wealth#Increased Financial Stability#Leveraging Skills and Passion#money#Moneymaking#Multiple Streams of Income#Passion#Passive Income#Wealth
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Abundance Accelerator - A Genuine Program To Real Financial Abundance?
There is a new manifestation product that is wildly popular and people are raving about the great results they are getting from it. But what is making this new program so special? It claims: “Finally!! Now You Can Put All Your Money Worries Behind You & Discover The ‘Universe’s KEY’ To Real Financial Abundance.” that’s a bold claim, so I was intrigued to try it out for myself to see if this was…

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#Abundance#Abundance Accelerator#Allanah Hunt#Attract Money#Attract Wealth#Financial Freedom#Instant Manifestation#Make Your Dream Come True#Manifest Money#Manifestation#Wealth
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AutoBNN: Probabilistic time series forecasting with compositional bayesian neural networks
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AutoBNN: Probabilistic time series forecasting with compositional bayesian neural networks

Posted by Urs Köster, Software Engineer, Google Research

Time series problems are ubiquitous, from forecasting weather and traffic patterns to understanding economic trends. Bayesian approaches start with an assumption about the data’s patterns (prior probability), collecting evidence (e.g., new time series data), and continuously updating that assumption to form a posterior probability distribution. Traditional Bayesian approaches like Gaussian processes (GPs) and Structural Time Series are extensively used for modeling time series data, e.g., the commonly used Mauna Loa CO2 dataset. However, they often rely on domain experts to painstakingly select appropriate model components and may be computationally expensive. Alternatives such as neural networks lack interpretability, making it difficult to understand how they generate forecasts, and don’t produce reliable confidence intervals.
To that end, we introduce AutoBNN, a new open-source package written in JAX. AutoBNN automates the discovery of interpretable time series forecasting models, provides high-quality uncertainty estimates, and scales effectively for use on large datasets. We describe how AutoBNN combines the interpretability of traditional probabilistic approaches with the scalability and flexibility of neural networks.
AutoBNN
AutoBNN is based on a line of research that over the past decade has yielded improved predictive accuracy by modeling time series using GPs with learned kernel structures. The kernel function of a GP encodes assumptions about the function being modeled, such as the presence of trends, periodicity or noise. With learned GP kernels, the kernel function is defined compositionally: it is either a base kernel (such as Linear, Quadratic, Periodic, Matérn or ExponentiatedQuadratic) or a composite that combines two or more kernel functions using operators such as Addition, Multiplication, or ChangePoint. This compositional kernel structure serves two related purposes. First, it is simple enough that a user who is an expert about their data, but not necessarily about GPs, can construct a reasonable prior for their time series. Second, techniques like Sequential Monte Carlo can be used for discrete searches over small structures and can output interpretable results.
AutoBNN improves upon these ideas, replacing the GP with Bayesian neural networks (BNNs) while retaining the compositional kernel structure. A BNN is a neural network with a probability distribution over weights rather than a fixed set of weights. This induces a distribution over outputs, capturing uncertainty in the predictions. BNNs bring the following advantages over GPs: First, training large GPs is computationally expensive, and traditional training algorithms scale as the cube of the number of data points in the time series. In contrast, for a fixed width, training a BNN will often be approximately linear in the number of data points. Second, BNNs lend themselves better to GPU and TPU hardware acceleration than GP training operations. Third, compositional BNNs can be easily combined with traditional deep BNNs, which have the ability to do feature discovery. One could imagine “hybrid” architectures, in which users specify a top-level structure of Add(Linear, Periodic, Deep), and the deep BNN is left to learn the contributions from potentially high-dimensional covariate information.
How might one translate a GP with compositional kernels into a BNN then? A single layer neural network will typically converge to a GP as the number of neurons (or “width”) goes to infinity. More recently, researchers have discovered a correspondence in the other direction — many popular GP kernels (such as Matern, ExponentiatedQuadratic, Polynomial or Periodic) can be obtained as infinite-width BNNs with appropriately chosen activation functions and weight distributions. Furthermore, these BNNs remain close to the corresponding GP even when the width is very much less than infinite. For example, the figures below show the difference in the covariance between pairs of observations, and regression results of the true GPs and their corresponding width-10 neural network versions.
Comparison of Gram matrices between true GP kernels (top row) and their width 10 neural network approximations (bottom row).
Comparison of regression results between true GP kernels (top row) and their width 10 neural network approximations (bottom row).
Finally, the translation is completed with BNN analogues of the Addition and Multiplication operators over GPs, and input warping to produce periodic kernels. BNN addition is straightforwardly given by adding the outputs of the component BNNs. BNN multiplication is achieved by multiplying the activations of the hidden layers of the BNNs and then applying a shared dense layer. We are therefore limited to only multiplying BNNs with the same hidden width.
Using AutoBNN
The AutoBNN package is available within Tensorflow Probability. It is implemented in JAX and uses the flax.linen neural network library. It implements all of the base kernels and operators discussed so far (Linear, Quadratic, Matern, ExponentiatedQuadratic, Periodic, Addition, Multiplication) plus one new kernel and three new operators:
a OneLayer kernel, a single hidden layer ReLU BNN,
a ChangePoint operator that allows smoothly switching between two kernels,
a LearnableChangePoint operator which is the same as ChangePoint except position and slope are given prior distributions and can be learnt from the data, and
a WeightedSum operator.
WeightedSum combines two or more BNNs with learnable mixing weights, where the learnable weights follow a Dirichlet prior. By default, a flat Dirichlet distribution with concentration 1.0 is used.
WeightedSums allow a “soft” version of structure discovery, i.e., training a linear combination of many possible models at once. In contrast to structure discovery with discrete structures, such as in AutoGP, this allows us to use standard gradient methods to learn structures, rather than using expensive discrete optimization. Instead of evaluating potential combinatorial structures in series, WeightedSum allows us to evaluate them in parallel.
To easily enable exploration, AutoBNN defines a number of model structures that contain either top-level or internal WeightedSums. The names of these models can be used as the first parameter in any of the estimator constructors, and include things like sum_of_stumps (the WeightedSum over all the base kernels) and sum_of_shallow (which adds all possible combinations of base kernels with all operators).
Illustration of the sum_of_stumps model. The bars in the top row show the amount by which each base kernel contributes, and the bottom row shows the function represented by the base kernel. The resulting weighted sum is shown on the right.
The figure below demonstrates the technique of structure discovery on the N374 (a time series of yearly financial data starting from 1949) from the M3 dataset. The six base structures were ExponentiatedQuadratic (which is the same as the Radial Basis Function kernel, or RBF for short), Matern, Linear, Quadratic, OneLayer and Periodic kernels. The figure shows the MAP estimates of their weights over an ensemble of 32 particles. All of the high likelihood particles gave a large weight to the Periodic component, low weights to Linear, Quadratic and OneLayer, and a large weight to either RBF or Matern.
Parallel coordinates plot of the MAP estimates of the base kernel weights over 32 particles. The sum_of_stumps model was trained on the N374 series from the M3 dataset (insert in blue). Darker lines correspond to particles with higher likelihoods.
By using WeightedSums as the inputs to other operators, it is possible to express rich combinatorial structures, while keeping models compact and the number of learnable weights small. As an example, we include the sum_of_products model (illustrated in the figure below) which first creates a pairwise product of two WeightedSums, and then a sum of the two products. By setting some of the weights to zero, we can create many different discrete structures. The total number of possible structures in this model is 216, since there are 16 base kernels that can be turned on or off. All these structures are explored implicitly by training just this one model.
Illustration of the “sum_of_products” model. Each of the four WeightedSums have the same structure as the “sum_of_stumps” model.
We have found, however, that certain combinations of kernels (e.g., the product of Periodic and either the Matern or ExponentiatedQuadratic) lead to overfitting on many datasets. To prevent this, we have defined model classes like sum_of_safe_shallow that exclude such products when performing structure discovery with WeightedSums.
For training, AutoBNN provides AutoBnnMapEstimator and AutoBnnMCMCEstimator to perform MAP and MCMC inference, respectively. Either estimator can be combined with any of the six likelihood functions, including four based on normal distributions with different noise characteristics for continuous data and two based on the negative binomial distribution for count data.
Result from running AutoBNN on the Mauna Loa CO2 dataset in our example colab. The model captures the trend and seasonal component in the data. Extrapolating into the future, the mean prediction slightly underestimates the actual trend, while the 95% confidence interval gradually increases.
To fit a model like in the figure above, all it takes is the following 10 lines of code, using the scikit-learn–inspired estimator interface:
import autobnn as ab model = ab.operators.Add( bnns=(ab.kernels.PeriodicBNN(width=50), ab.kernels.LinearBNN(width=50), ab.kernels.MaternBNN(width=50))) estimator = ab.estimators.AutoBnnMapEstimator( model, 'normal_likelihood_logistic_noise', jax.random.PRNGKey(42), periods=[12]) estimator.fit(my_training_data_xs, my_training_data_ys) low, mid, high = estimator.predict_quantiles(my_training_data_xs)
Conclusion
AutoBNN provides a powerful and flexible framework for building sophisticated time series prediction models. By combining the strengths of BNNs and GPs with compositional kernels, AutoBNN opens a world of possibilities for understanding and forecasting complex data. We invite the community to try the colab, and leverage this library to innovate and solve real-world challenges.
Acknowledgements
AutoBNN was written by Colin Carroll, Thomas Colthurst, Urs Köster and Srinivas Vasudevan. We would like to thank Kevin Murphy, Brian Patton and Feras Saad for their advice and feedback.
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